NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections of NCERT Exemplar Class 11 Maths. Here we have given NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections.

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections

Short Answer Type Questions

Q1. Find the equation of the circle which touches the both axes in first quadrant and whose radius is a.
Sol:
Conic Sections Class 11 Important Questions NCERT

Q2. Show that the point (x, y) given by  \(x=\frac { 2at }{ 1+{ t }^{ 2 } }   \) and \(y=\frac { 1-{ t }^{ 2 } }{ 1+{ t }^{ 2 } }  \) lies on a circle .
NCERT Exemplar Class 11 Maths Conic Sections

NCERT Exemplar Class 11 Maths Conic Sections

Q3. If a circle passes through the point (0, 0) (a, 0), (0, b) then find the coordinates of its centre.
Sol: We have circle through the point A(0, 0), B(a, 0) and C(0, b).
Clearly triangle is right angled at vertex A.
Conic Sections Class 11 Exemplar NCERT

So, centre of the circle is the mid point of hypotenuse BC which is (a/2, b/2)

Conic Sections Class 11 Exemplar NCERT

Q4. Find the equation of the circle which touches x-axis and whose centre is (1,2).
Sol: Given that, circle with centre (1,2) touches x-axis.
Radius of the circle is, r = 2
So, the equation of the required circle is:
(x – l)2 + (y – 2)2 = 22
=>x2-2x + 1 + y2-4y + 4 = 4
=> x2 + y2 – 2x-4y + 1 = 0

Q5. If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then find the radius of the circle.
Sol: Given lines are 6x – 8y + 8 = 0 and 6x – 8y – 7 = 0.
These parallel lines are tangent to a circle.
NCERT Exemplar Class 11 Conic Sections Solutions

Q6. Find the equation of a circle which touches both the axes and the line 3x – 4y + 8 = 0 and lies in the third quadrant.
Important Questions Of Conic Sections Class 11

NCERT Exemplar Class 11 Conic Sections Solutions

Q7. If one end of a diameter of the circle x2 + y2 -4x -6y + 11 = 0 is (3,4), then find the coordinate of the other end of the diameter.
Sol: Given equation of the circle is:
Conic Sections Class 11 Extra Questions NCERT

Q8. Find the equation of the circle having (1, -2) as its centre and passing through 3x +y= 14, 2x + 5y = 18.
NCERT Exemplar Class 11 Maths Chapter 11 Solutions

Important Questions Of Conic Sections Class 11

Q9. If the line y= √3 x + k touches the circle x2 + y2 = 16, then find the value of
Sol:
Given line is y = √3 x + k and the circle is x2 + y2 = 16.
Class 11 Conic Sections Extra Questions NCERT

Q10. Find the equation of a circle concentric with the circle x2 +y2 – 6x + 12y + 15 = 0 and has double of its area.
Class 11 Maths Chapter 11 Extra Questions NCERT

Conic Sections Class 11 Extra Questions NCERT

Q11. If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity.
Conic Sections Exemplar Solutions NCERT

Q12. Given the ellipse with equation 9X2 + 25y2 = 225, find the eccentricity and foci.
Questions On Conic Sections Class 11 NCERT

NCERT Exemplar Class 11 Maths Chapter 11 Solutions

Q13. If the eccentricity of an ellipse is 5/8 and the distance between its foci is 10, then find latus rectum of the ellipse.
Important Questions For Class 11 Maths Conic Sections

Class 11 Conic Sections Extra Questions NCERT

Q14. Find the equation of ellipse whose eccentricity is 2/3, latus rectum is 5 and thecentre is (0, 0).
NCERT Exemplar Class 11 Maths

Class 11 Maths Chapter 11 Extra Questions NCERT

Q15. Find the distance between the directrices of the ellipse \(\frac { { x }^{ 2 } }{ 36 } +\quad \frac { { y }^{ 2 } }{ 20 } \quad =\quad 1  \)
Class 11 Conic Section Questions NCERT

Q16. Find the coordinates of a point on the parabola y2 = 8x whose focal distance is 4.
Conic Sections Exemplar NCERT Class 11

Q17. Find the length of the line-segment joining the vertex of the parabola y2 = 4ax and a point on the parabola where the line-segment makes an angle 6 to the x-axis.
Sol: Given equation of the parabola isy2 = 4ax.
Let the point on the parabola be P(x1,,y1).
Conic Sections Important Questions NCERT Class 11
NCERT Exemplar Conic Sections Class 11

Q18. If the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-1

Q19. If the line y = mx + 1 is tangent to the parabola y2 = 4x then find the value of m.
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-2

Q20. If the distance between the foci of a hyperbola is 16 and its eccentricity is √2, then obtain the equation of the hyperbola.
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-3

Q21. Find the eccentricity of the hyperbola 9y2 – 4x2 =36
Sol: We have the hyperbola:9y2 – 4x2 = 36
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-4

Q22. Find the equation of the hyperbola with eccentricity 3/2 and foci at (±2, 0).
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-5

Long Answer Type Questions

Q23. If the lines 2x – 3y = 5 and 3x-4y = 7 are the diameters of a circle of area 154 square units, then obtain the equation of the circle.
Sol: Given that lines 2x – 3y – 5 = 0 and 3x – 4y -1 = 0 are diameters of the circle. Solving these lines we get point of intersection as (1, -1), which is centre of the circle.
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-6

Q24. Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y – 4x + 3 = 0.
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-7

Q25. Find the equation of a circle whose centre is (3, -1) and which cuts off a chord of length 6 units on the line 2x — 5y+ 18 = 0.

Sol: Given centre of the circle 0(3, -1)
Chord of the circle is AB.
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-8
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-9

Q26. Find the equation of a circle of radius 5 which is touching another circle x2 + y2 – 2x – 4y – 20 = 0 at (5, 5).
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-10

Q27. Find the equation of a circle passing through the point (7, 3) having radius 3 units and whose centre lies on the line y = x -1.
Sol:
Given that circle passes through the point A(7, 3) and its radius is 3.
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-11

Q28. Find the equation of each of the following parabolas.
(i) Directrix, x = 0, focus at (6, 0)
(ii) Vertex at (0,4), focus at (0, 2)
(iii) Focus at (-1, -2), directrix x – 2y + 3 = 0
Sol: We know that the distance of any point on the parabola from its focus and its directrix is same.
(i) Given that, directrix, x = 0 and focus = (6, 0)
So, for any point P(x, y) on the parabola
Distance of P from directrix = Distance of P from focus =>  x2 = (x — 6)2 + y2
=>         y2– 12x + 36 = 0
(ii) Given that, vertex = (0,4) and focus = (0, 2)
Now distance between the vertex and directrix is same as the distance between the vertex and focus.
Directrix is y – 6 = 0
For any point of P(x, y) on the parabola
Distance of P from directrix = Distance of P from focus
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-12

Q29. Find the equation of the set of all points the sum of whose distances from the points (3, 0) and (9, 0) is 12.

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-13

Q30. Find the equation of the set of all points whose distance from (0,4) are 2/3 of their distance from the line y = 9.

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-14

Q31. Show that the set of all points such that the difference of their distances from (4, 0)and (-4, 0) is always equal to 2 represent a hyperbola.

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NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-16
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-17

True/False Type Questions

Q33. The line x + 3y = 0 is a diameter of the circle x2 + y2 + 6x + 2y = 0.
Sol: False
Given equation of the circle is x2 + y2 + 6x + 2y = 0
Centre = (-3, -1)
Clearly, it does not lie on the line x + 3y = 0 as -3 + 3(-l) = -6.
So, this line is not diameter of the circle.

Q34. The shortest distance from the point (2, -7) to the circle x +y2 – 1 4jc – lOy- 151 = 0 is equal to 5.
Sol: False
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-18

Q35. If the line lx + my = 1 is a tangent to the circle x2 + y2 = a2, then the point (1, m) lies on a circle.
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-19

Q36. The point (1,2) lies inside the circle x2 + y2 – 2x + 6y + 1 = 0.
Sol: False
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-20

Q37. The line lx+ my + n = 0 will touch the parabola^2 = 4 ax if In = am2.
Sol: True
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-21
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-22
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-23
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-24
Fill in the Blanks Type Questions

Q41. The equation of the circle having centre at (3, -4) and touching the line 5x + 12y- 12 = 0 is ______.

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-25

Q42. The equation of the circle circumscribing the triangle whose sides are the lines y = x + 2, 3y = 4x, 2y = 3x is   _______.
Given equation of line are:
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-26

Q43. An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the length of the string and distance between the pins are _____ .
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-27
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-28

Q44. The equation of the ellipse having foci (0,1), (0, -1) and minor axis of length 1 is ___ .
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-29

Q45. The equation of the parabola having focus at (-1, -2) and the directrix x – 2y + 3 = 0 is______ .
Sol:
Given that, focus at S(-l, -2) and directrix is x – 2y + 3 = 0
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-30

Q46. The equation of the hyperbola with vertices at (0, ±6) and eccentricity 5/3 ________ and its foci are _____    .

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-31

Objective Type Questions

Q47. The area of the circle centred at (1,2) and passing through (4, 6) is
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-32

Q48. Equation of a circle which passes through (3, 6) and touches the axes is
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-33

Q49. Equation of the circle with centre on the j-axis and passing through the origin and the point (2, 3) is

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-34

Q50. The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-35

Q51. If the focus of a parabola is (0, -3) and its directrix is y = 3, then its equation is

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-36

Q52. If the parabola y2 = 4ax passes through the point (3, 2), then the length of its latus rectum is
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-37

Q53. If the vertex of the parabola is the point (-3, 0) and the directrix is the line x + 5 = 0, then its equation is
(a) y2 = 8(x + 3)
(b) x2 = 8(y + 3)
(c) y2 = -8(x + 3)
(d) y2 = 8(x + 5)
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-38

Q54. The equation of the ellipse whose focus is (1, -1), the directrix the line x-y-3 = 0 and eccentricity 1/2 is
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-39

Q55. The length of the latus rectum of the ellipse 3x2 +y2 = 12 is
(a) 4       
(b) 3       
(c) 8       
(d) 4/√3

NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-40
NCERT Exemplar Class 11 Maths Chapter 11 Conic Sections-41

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