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  4. The points A(3 , 6) and B lie on the parabola y2=4ax , such that the chord AB subtends 90° at the origin, then the length of the chord AB is equal to

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Q. The points $A\left(3 , 6\right)$ and $B$ lie on the parabola $y^{2}=4ax$ , such that the chord $AB$ subtends $90^\circ $ at the origin, then the length of the chord $AB$ is equal to

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Solution:

Solution
Since the chord subtends a right angle at the origin,
$\therefore t_{1}t_{2}=-4$
Now, the point $A$ lies on the parabola,
$\therefore 36=4a\left(3\right)\Rightarrow a=3$
i.e. $A\left(3 , 6\right)=\left(3 t_{1}^{2} , 6 t_{1}\right)$
$\Rightarrow t_{1}=1\Rightarrow t_{2}=-4$
So, $B\equiv \left(48 , - 24\right)$
Hence, the length of the chord $AB=15\sqrt{13}$ units