Mathematics - Parabola Question with Solution | TestHub

Through the vertex ' O ' of parabola $y^2=4x$, chords OP and OQ are drawn at right angles to one another. Then the locus of middle point of PQ is a parabola with Latus rectum $\lambda$, then $\lambda$ equals

$$k=\frac{2\left(t_1+t_2\right)}{2}=t_1+t_2$$

Also $t_1{t}_2=-4\Rightarrow 2h+{\left(t_1+t_2\right)}^2-2t_1{t}_2$

$$\begin{array}{rlr}& 2h=k^2+8& y^2=2(x-4)\end{array}$$

∴ Latus rectum $=2$