Important Questions for CBSE Class 11 Maths Chapter 11

CBSE Class 11 Maths Chapter-11 Important Questions - Free PDF Download

1 Marks Questions

1. Find the equation of a circle with centre (P,Q) & touching the y axis

Ans.

2.Find the equations of the directrix & the axis of the parabola

Ans.

3.Find the coordinates of the foci of the ellipse

Ans.

4.Find the eccentricity of the hyperbola:

Ans.

5.Find the equation of a circle with centre & touching axis?

Ans.

6.Find the lengths of axes of

Ans.Units & units

7.Find the length of the latus rectum of

Ans.4 units

8.Find the length of the latus rectum of the parabola

Ans.units

9.The equation represent a circle find its centre

Ans.

10.Find the equation of the parabola with focus & directrix

Ans.

11.Find the coordinates of the foci of

Ans.

12.Find the coordinates of the vertices of

Ans.

13.Find the coordinates of the vertices of

Ans.

14.Find the eccentricity of ellipse

Ans.

15.Find the length of the latus rectum of

Ans.

16.Find the length of minor axis of

Ans.

17.Find the centre of the circles

None of these

Ans.

18.Find the radius of circles

Ans.

19.Find the length of latcus rectum of

None of these

Ans.22

20.Find the length of latcus rectum of

None of these

Ans. Units

4 Marks Questions

1.Show that the equation represent a circle, also find its centre & radius?

Ans. This is of the form

So, centre of the circle

Radius of the circle

units

2.Find the equation of an ellipse whose foci are & the eccentricity is ?

Ans. Let the required equation of the ellipse be

let the foci be

Now

Hence equation is

3.Find the equation of an ellipse whose vertices are &

Ans. Let equation be

& its vertices are

Let

Then

Now

Hence the equation is

4.Find the equation of hyperbola whose length of latus rectum is 36 & foci are

Ans. Clearly C = 12

Length of cat us rectum

Now

This

Hence,

5.Find the equation of a circle drawn on the diagonal of the rectangle as its diameter, whose sides are

Ans. Let ABCD be the given rectangle &

Then

So the equation of the circle with AC as diameter is given as

6.Find the coordinates of the focus & vertex, the equations of the diretrix & the axis & length of latus rectum of the parabola

Ans.

So,

So it is case of downward parabola

o, foci is

Its vertex is

So,

Its axis is y – axis, whose equation is length of lotus centum

units.

7.Show that the equation represents a circle. Also find its centre & radius.

Ans.

Where,

Hence, centre of circle

Radius of circle

units

8.Find the equation of the parabola with focus at & directrix is

Ans.Focus lies to the right hand side of the origin

So, it is right hand parabola.

Let the required equation be

So,

9.Find the equation of the hyperbola with centre at the origin, length of the transverse axis 18 & one focus at (0,4)

Ans.Let its equation be

Clearly, C = 4.

length of the transverse axis

Also,

So,

So, equation is

10.Find the equation of an ellipse whose vertices are the foci are

Ans.Let the equation be

& a = 13

Let its foci be then

So,

So, equation be

11.Find the equation of the ellipse whose foci are & length of whose major axis is 10

Ans. Let the required equation be

Let

Its foci are

Also, a = length of the semi- major axis =

Now,

Then,

Hence the required equation is

12.Find the equation of the hyperbola with centre at the origin, length of the transverse axis 8 & one focus at (0,6)

Ans. Let its equation by

Clearly, C = 6

& length of the transverse axis

Also,

So,

Hence, the required equation is

13.Find the equation of the hyperbola whose foci are at & the length of whose conjugate axis is

Ans. Let it equation be

Let it foci be

Length of conjugate axis

Also,

Hence, required equation is

14.Find the equation of the hyperbola whose vertices are & foci are

Ans. The vertices are

But it is given that the vertices are

Let its foci be

But it is given that the foci are

Now

Then

Hence the required equation is

15.Find the equation of the ellipse for which & whose vertices are

Ans. Its vertices are therefore a =10

Let

Then,

Now,

Hence the required equation is

16.Find the equation of the ellipse, the ends of whose major axis are & the ends of whose minor axis are

Ans. Its vertices are & therefore, a = 5 ends of the minor axis are

i.e length of minor axis = 25 units

Now,

Hence, the required equation

16.Find the equation of the parabola with vertex at the origin & y+5 = 0 as its directrix. Also, find its focus

Ans. Let the vertex of the parabola be

Now

Then the directrix is a line parallel

To the axis at a distance of 5 unite below the axis so the focus is

Hence the equation of the parabola is

Where a = 5i.e,

17.Find the equation of a circle, the end points of one of whose diameters are

Ans. Let the end points of one of whose diameters are is given by

Hence

The required equation of the circle is

18.Find the equation of ellipse whose vertices are & the foci are

Ans. Let the required equation be 5.

Its vertices are & therefore a = 13

Let its foci be then C = 5

This

Hence, the required equation is

19.Find the equation of the hyperbola whose foci are & the transverse axis is of length 8.

Ans. Let the required equation be

Length of its Trans verse axis =2a

Let its foci be

Then C = 5

This

Hence, the required equation is

20.Find the equation of a circle, the end points of one of whose diameters are

Ans. Let the equation be

Hence

21.If eccentricity is & foci are find the equation of an ellipse.

Ans. Let the required equation of the ellipse be

Let its foci be Then C =7

Also,

Now

Hence the required equation is

22.Find the equation of the hyperbola where foci are & the transverse axis is of length

Ans. Let the required equation be

Length of its transverse axis

Let its foci be

Then C = 5

Hence the required equation is

23.Find the length of axes & coordinates of the vertices of the hyperbola

Ans. The equation of the given hyperbola is

Comparing the given equation with we get

Length of transverse axis =units

Length of conjugate axis = units

The coordinators of the vertices are

24.Find the lengths of axes & length of lat us rectum of the hyperbola,

Ans. The given equation is means hyperbola

Comparing the given equation with we get

Length of transverse axis units

Length of conjugate axis units

The coordinates of the vertices are i.e

25.Find the eccentricity of the hyperbola of

Ans. As in above question

So, c = 5

Then

26.Find the equation of the hyperbola with centre at the origin, length of the trans verse axis 6 & one focus at

Ans. Let its equation be

Clearly c = 4

Length of transverse axis

Also,

Then

Hence, the required equation is

27.Find the equation of the ellipse, the ends of whose major axis are & at the ends of whose minor axis are

Ans. Let the required equation be

Its vertices are

Ends of minor axis are

i.e length of the minor axis = 8 units

Now,

Hence the required equation is

28.Find the equation of the parabola with focus at & directrix

Ans. Focus lies on the axis hand side of the origin so, it is a right handed parabola. Let the required equation be

Than, a = 4

Hence, the required equation is

29.If is a chord of the circle find the equation of the circle with this chord as a diameter

Ans.

Putting in we get

Now,

the points of intersection of the given chord & the given circle are

the required equation of the circle with AB as diameter is

6 Marks Questions

1. Find the length of major & minor axis- coordinate’s of vertices & the foci, the eccentricity & length of latus rectum of the ellipse

Ans.

Dividing by 16,

Thus

(i)Length of major axis units

Length of minor axis units

(ii)Coordinates of the vertices are

(iii)Coordinates of foci are

(iv)Eccentricity,

(v)Length of latus rectum units

2. Find the lengths of the axis , the coordinates of the vertices & the foci the eccentricity & length of the lat us rectum of the hyperbola

Ans.

So,

(i) Length of transverse axis

Length of conjugate axis

(ii) The coordinates of vertices are

(iii) The coordinates of foci are

(iv) Eccentricity,

(v) Length of the lat us rectum units

3. Find the area of the triangle formed by the lines joining the vertex of the parabola to the ends of its latus rectum.

Ans. The vertex of the parabola

Comparing with we get the coordinates of its focus S are .

Clearly, the ends of its latus rectum are :

area of

units.

4. A man running in a race course notes that the sum of the distances of the two flag posts from him is always 12 m & the distance between the flag posts is 10 m. find the equation of the path traced by the man.

Ans. We know that on ellipse is the locus of a point that moves in such a way that the sum of its distances from two fixed points (caked foci) is constant.

So, the path is ellipse.

Let the equation of the ellipse be

where

Clearly,

Hence, the required equation is

5. An equilateral triangle is inscribed in the parabola so that one angular point of the triangle is at the vertex of the parabola. Find the length of each side of the triangle.