In This Post we are  providing Chapter- 11 CONIC SECTIONS NCERT MOST IMPORTANT QUESTIONS for Class 11 MATHS which will be beneficial for students. These solutions are updated according to 2021-22 syllabus. These MCQS  can be really helpful in the preparation of Board exams and will provide you with a brief knowledge of the chapter.

NCERT MOST IMPORTANT QUESTIONS CONIC SECTIONS

1.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 

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

Ans. Let equation be 

& its vertices are 

Let 

Then 

Now 

Hence the equation is 

3.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, 

4.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

5.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.

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

Ans.

So 

Where, 

Hence, centre of circle &

Radius of circle 

units

7.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, 

8.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 

9.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 

10.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 

11.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 

12.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 

13.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 

14.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 

15.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 

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