NCERT Class 11-Math՚s: Exemplar Chapter – 11 Conic Sections Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 13:

The area of the triangle formed by the lines joining the vertex of the parabola to the ends of its latus rectum is

(A) . units

(B) . units

(C) . units

(D) . units

The correct option is (C) .

From the figure, OPQ represent the triangle whose area is to be determined. The area of the triangle

Question 14:

The equations of the lines joining the vertex of the parabola to the points on it which have abscissa are

(A)

(B)

(C)

(D)

(B) is the correct choice.

Let P and Q be points on the parabola and OP, OQ be the lines joining the vertex O to the points P and Q whose abscissa are 24.

Thus

or .

Therefore the coordinates of the points P and Q are and respectively. Hence the lines are

Question 15:

The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points and is

(A)

(B)

(C)

(D)

(B) is the correct choice.

Let be the equation of the ellipse. Then according to the given conditions, we have

Which gives

Hence, required equation of ellipse is .

Question 16:

The length of the transverse axis along x-axis with centre at origin of a hyperbola is and it passes through the point . The equation of the hyperbola is

(A)

(B)

(C)

(D) None of these