Question

The centre of an ellipse is C and PN is any ordinate and A, A' are the end points of major axis, then the value of $\frac{PN^{2}}{AN.A'N}$ is

• A. $\frac{b^{2}}{a^{2}}$
• B. $\frac{a^{2}}{b^{2}}$
• C. a² + b²
• D. 1

Answer 1

Answer: (A)

$\frac{b^{2}}{a^{2}}$

Answer 2

Let P(a cos q, b sin q)

PN = b sin q

Ž AN = a – a cos q

Ž A'N = a + a cos q

Ž$\frac{PN^{2}}{AN \cdot A'N} = \frac{b^{2}\sin^{2}\theta}{(a - a\cos\theta)(a + a\cos\theta)}$ = $\frac{b^{2}}{a^{2}}$