# NCERT Class 11-Math's: Exemplar Chapter –11 Conic Sections Part 7

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**Question 23:**

The eccentricity of the hyperbola which passes through the points and is ________________ .

**Answer:**

Given that the hyperbola is passing through the points and , so we get and .

Again, we know that . This gives

Or

Or.

## 11.3 EXERCISE

## Short Answer Type

**Question 1:**

Find the equation of the circle which touches the both axes in first quadrant and whose radius is *a*.

**Answer:**

**Question 2:**

Show that the point given by and lies on a circle for all real values of *t* such that where *a* is any given real numbers.

**Answer:**

Squaring both the equations,

Adding both the equations,

The equation of a circle having centre , having radius as “” units, is

Centre Radius units

Hence proved

**Question 3:**

If a circle passes through the point then find the coordinates of its centre.

**Answer:**

**Question 4:**

Find the equation of the circle which touches *x*-axis and whose centre is .

**Answer:**

**Question 5:**

If the lines and are tangents to a circle, then find the radius of the circle.

[**Hint:** Distance between given parallel lines gives the diameter of the circle.]

**Answer:**

**Question 6:**

Find the equation of a circle which touches both the axes and the line 3*x* – 4*y* + 8 = 0 and lies in the third quadrant.

[Hint: Let be the radius of the circle, then will be centre and perpendicular distance from the centre to the given line gives the radius of the circle.]

**Answer:**

**Question 7:**

If one end of a diameter of the circle is , then find the coordinate of the other end of the diameter.

**Answer:**

**Question 8:**

Find the equation of the circle having as its centre and passing through

**Answer:**