Question

Length of focal chord of y² = 4ax inclined at an angle 30⁰ with x-axis is : {L.R. is latus rectum}

• A. L.R.
• B. 2L.R.
• C. 4L.R.
• D. 8L.R.

Answer 1

Answer: (C)

4L.R.

Answer 2

Equation of focal chord (y – 0) = tan 30º(x – a)

̃ y = $\frac{x}{\sqrt{3}}$–$\frac{a}{\sqrt{3}}$ ̃ m = $\frac{1}{\sqrt{3}}$, c = –$\frac{a}{\sqrt{3}}$

Length = $\frac{4}{m^{2}}$$\sqrt{a(a–mc)}$

= $\frac{4}{1/3}\sqrt{1 + \frac{1}{3}}\sqrt{a\left( a + \frac{a}{3} \right)}$

= 12a$\left( 1 + \frac{1}{3} \right)$ = 16a