Question

If $\left(t^2, 2 t\right)$ is one end of a focal chord of the parabola $y^2=4 x$ then the length of the focal chord will be-

• A. $\left(t+\frac{1}{t}\right)^2$
• B. $\left(t+\frac{1}{t}\right) \sqrt{\left(t^2+\frac{1}{t^2}\right)}$
• C. $\left(t-\frac{1}{t}\right) \sqrt{\left(t^2+\frac{1}{t^2}\right)}$
• D. none

Answer 1

Answer: (A)

Given $\left(t^2, 2 t\right)$ be one end of focal chord then other end be $\left(\frac{1}{t^2}, \frac{-2}{t}\right)$
length of focal chord
$=\sqrt{\left(t^2-\frac{1}{t^2}\right)^2+\left(2 t+\frac{2}{t}\right)^2}=\left(t+\frac{1}{t}\right)^2$