# NCERT Class 11-Math's: Exemplar Chapter –11 Conic Sections Part 8

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**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:**