Question

Two tangents to a parabola are $x-y=0$ and $x+y=0.$ If $(2,3)$ is focus of parabola then length of latus rectum of the parabola is

• A. $\frac{5}{2\sqrt{13}}$ units
• B. $\frac{7}{2\sqrt{13}}$ units
• C. $\frac{14}{\sqrt{13}}$ units
• D. None of these

Answer 1

The correct option is D None of these

We have,

$x-y=0x+y=0Imageof\left(2,3\right)iny=xis\left(3,2\right)whichlieondirectEquationofdirection:y=\frac{2}{3}x3y-2x=0L_R=2\times \frac{19-41}{\sqrt{13}}=\frac{2\times 5}{\sqrt{13}}$

$lengthoflatusrectum=\frac{10}{\sqrt{13}}$

$Hence,optionDiscorrectanswer.$