If a normal chord at a point $t(
eq 0)$ on the parabola $y^2=9 x$ subtends a right angle at its vertex, then $t=$

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Aicharya · Accepted Answer

Equation of given parabola is Equation of normal chord at a point $t(
eq 0)$ on the parabola (i) is $\because$ The chord (ii) subtends a right angle at vertex of parabola $V(0,0)$, so first homogenise the parabola (i) with the help of line (ii), we get $ \begin{array}{rlrl} & 	ext { So, } & 1-\frac{9 t}{\frac{9}{2} t+\frac{9}{4} t^3} & =0 \ \Rightarrow & 1-\frac{1}{\frac{1}{2}+\frac{t^2}{4}} & =0 \ \Rightarrow & \frac{1}{2}+\frac{t^2}{4} & =1 \ \Rightarrow & t^2=2 \Rightarrow t & = \pm \sqrt{2} \end{array} $ Hence, option (d) is correct

If a normal chord at a point $t(\neq 0)$ on the parabola $y^2=9 x$ subtends a right angle at its vertex,…

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