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

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**Question 46**:

The equation of the hyperbola with vertices at and eccentricity is ________and its foci are ________.

**Answer**:

## Choose the Correct Answer Out of the Given Four Options (M. C. Q.) in Exercises 47 to 59

**Question 47**:

The area of the circle centred at and passing through is

(A)

(B)

(C)

(D) None of these

**Answer: (C)**

**Question 48**:

Equation of a circle which passes through and touches the axes is

(A)

(B)

(C)

(D) None of these

**Answer: (C)**

**Question 49**:

Equation of the circle with centre on the *y*-axis and passing through the origin and the point is

(A)

(B)

(C)

(D)

**Answer: (C)**

**Question 50**:

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length is

(A)

(B)

(C)

(D)

[Hint: Centroid of the triangle coincides with the centre of the circle and the radius of the circle is of the length of the median]

**Answer: (C)**

**Question 51**:

If the focus of a parabola is and its directrix is , then its equation is

(A)

(B)

(C)

(D)

**Answer: (A)**

**Question 52**:

If the parabola passes through the point , then the length of its latus rectum is

(A)

(B)

(C)

(D)

**Answer: (B)**

**Question 53**:

If the vertex of the parabola is the point and the directrix is the line , then its equation is

(A)

(B)

(C)

(D)

**Answer: (A)**

**Question 54**:

The equation of the ellipse whose focus is , the directrix the line and eccentricity is

(A)

(B)

(C)

(D) None

**Answer: (A)**

**Question 55**:

The length of the latus rectum of the ellipse is

(A)

(B)

(C)

(D)

**Answer: (D)**