Question

Length of focal cord on parabola $y^2=x$, whichis making an angle of ${30}^{\circ }$ with x-axis is

• A. 2
• B. 5
• C. 4
• D. 7

Answer 1

The correct option is C 4

The length of a focal chord of the parabola $y^2=4ax$ making an angle $\theta$ with the axis of the parabola is

Length of the focal chord if

$a\sqrt{{(t^2-\frac{1}{t^2})}^2+4{(t+\frac{1}{t})}^2}$

$=a{(t+\frac{1}{t})}^2$

Now $\tan \theta =\frac{2(t+\frac{1}{t})}{t^2-\frac{1}{e^2}}$

$=\frac{2}{t-\frac{1}{t^2}}$

$={(t+\frac{1}{t})}^2={(t-\frac{1}{t})}^2+4$

$=4{\cot }^2\theta +4$

$=4a{\csc }^2\theta$

Thus length is 4.