Question

If P(q), Q $\left( \theta + \frac{\pi}{2} \right)$ are points on ellipse and a is angle

between normals at P and Q then –

• A. $2\sqrt{1–e^{2}}$ = e sin2 2q tan a
• B. $2\sqrt{1–e^{2}}$ = e sin2q. tan 2a
• C. $\sqrt{1–e^{2}}$ = 2e2 sin2 2q. tana
• D. $2\sqrt{1–e^{2}}$ = e2 sin2 2q. tana

Answer 1

Answer: (D)

$2\sqrt{1–e^{2}}$ = e2 sin2 2q. tana

Answer 2

Slope of normal at P = $\frac{a\sin\theta}{b\cos\theta}$ = m1 (let).

Slope of normal at Q = $\frac{–a\sin\theta}{b\cos\theta}$ = m2(let)

Therefore tan a = $\frac{m_{1}–m_{2}}{1 + m_{1}m_{2}} = \frac{2t}{ae}$ = cosec 2q

$2\sqrt{1–e^{2}}$ = e2 sin2 2q. tan a.