Question

For the parabola $y^2=4ax$, the length of the chord passing through the vertex and inclined to the x-axis at angle $\theta$, is

• A. $\frac{4a\cos \theta }{{\sin }^2\theta }$
• B. $\frac{4a\cos \theta }{{\cos }^2\theta }$
• C. $a{\sec }^2\theta$
• D. $a{\csc }^2\theta$

Answer 1

Answer: (A)

$\frac{4a\cos \theta }{{\sin }^2\theta }$

Let the length of chord be L then the coordinate of point where chord cut the parabola is

$x_1=L\cos \theta y_1=L\sin \theta$

We have the parabola equation as follow

$y^2=4ax$

This point will satisfy the equation of parabola

$\Rightarrow {\left(L\sin \theta \right)}^2=4a\left(L\cos \theta \right)\Rightarrow L=\frac{4a\cos \theta }{{\sin }^2\theta }$

Hence the correct option is A