Question

If $\left(t^2,2t\right)$ is one end of a focal chord of the parabola $y^2=4x$ 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 $\left(t^2,2t\right)$ be one end of focal chord then other end be $\left(\frac{1}{t^2},\frac{-2}{t}\right)$
length of focal chord
$=\sqrt{{\left(t^2-\frac{1}{t^2}\right)}^2+{\left(2t+\frac{2}{t}\right)}^2}={\left(t+\frac{1}{t}\right)}^2$