# NCERT Class 11-Math՚S: Exemplar Chapter – 11 Conic Sections Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

Glide to success with Doorsteptutor material for IMO Class-11: fully solved questions with step-by-step explanation- practice your way to success.

**Question 9**:

If the line touches the circle , then find the value of .

[**Hint**: Equate perpendicular distance from the centre of the circle to its radius] .

**Answer**:

**Question 10**:

Find the equation of a circle concentric with the circle and has double of its area.

[**Hint**: concentric circles have the same centre.]

**Answer**:

**Question 11**:

If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity

**Answer**:

**Question 12**:

Given the ellipse with equation , find the eccentricity and foci.

**Answer**:

**Question 13**:

If the eccentricity of an ellipse is and the distance between its foci is 10, then find latus rectum of the ellipse.

**Answer**:

**Question 14**:

Find the equation of ellipse whose eccentricity is , latus rectum is 5 and the centre is .

**Answer**:

**Question 15**:

Find the distance between the directrices of the ellipse .

**Answer**:

**Question 16**:

Find the coordinates of a point on the parabola whose focal distance is .

**Answer**:

**Question 17**:

Find the length of the line-segment joining the vertex of the parabola and a point on the parabola where the line-segment makes an angle to the .

**Answer**:

**Question 18**:

If the points and are respectively the vertex and focus of a parabola, then find the equation of the parabola.

**Answer**:

**Question 19**:

If the line is tangent to the parabola then find the value of .

[**Hint**: Solving the equation of line and parabola, we obtain a quadratic equation and then apply the tangency condition giving the value of ] .

**Answer**:

**Question 20**:

If the distance between the foci of a hyperbola is and its eccentricity is , then obtain the equation of the hyperbola.

**Answer**:

**Question 21**:

Find the eccentricity of the hyperbola .

**Answer**:

**Question 22**:

Find the equation of the hyperbola with eccentricity and foci at .

**Answer**: