If tangents at $A$ and $B$ on the parabola $y^{2} = 4ax$ intersect at point $C$, then ordinates of $A,\ C$ and $B$ are

Question

Dr. Abubacker · Accepted Answer

(a)
Let $A \equiv \left( {at}_{1}^{2},\ {2at}_{1} \right),\ B \equiv ({at}_{2}^{2},\ {2at}_{2})$
Tangents, at $A$ and $B$ will intersect at the point $C$, whose coordinate is given by $\left\{ {at}_{1}t_{2},\ a\left( t_{1} + t_{2} \right) \right\}$. Clearly, ordinates of $A,\ C$ and $B$ are always in AP

Q. If tangents at $A$ and $B$ on the parabola $y^{2} = 4ax$ intersect at point $C$, then ordinates of $A,\ C$ and $B$ are

Explanation

Reviewed by Dr. Abubacker

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