Question

If length of focal chord of y² = 4ax is l, then angle between axis of parabola and focal chord is

• A. ± sin^–1$\sqrt{\frac{2a}{\mathcal{l}}}$
• B. ± sin^–1$\sqrt{\frac{4a}{\mathcal{l}}}$
• C. ± tan^–1$\sqrt{\frac{4a}{\mathcal{l}}}$
• D. None of these

Answer 1

Answer: (B)

± sin^–1$\sqrt{\frac{4a}{\mathcal{l}}}$

Answer 2

Let any point on focal chord is P(h, k)

where h = a + r cos a

k = r sin a

\ Put (h, k) in y² = 4ax

̃ r² sin² a = 4a (a + r cos a)

\ r₁ + r₂ =$\frac{4a\cos\alpha}{\sin^{2}\alpha}$, r₁r₂ = $\frac{- 4a^{2}}{\sin^{2}\alpha}$

Now here length of focal chord is

l = |r₁| + |r₂|

= r₁ –r₂

= $\sqrt{(r_{1} + r_{2})^{2} - 4r_{1}r_{2}}$

\ l = 4a/sin²a