If {y_1} and {y_2} are the ordinates of two p | vedclass

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(B) Let the coordinates of points $P$ and $Q$ on the parabola $y^2 = 4ax$ be $(at_1^2, 2at_1)$ and $(at_2^2, 2at_2)$ respectively.Thus,the ordinates a

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${y_1}, {y_3}, {y_2}$ are in $A.P.$

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(B) Let the coordinates of points $P$ and $Q$ on the parabola $y^2 = 4ax$ be $(at_1^2, 2at_1)$ and $(at_2^2, 2at_2)$ respectively.Thus,the ordinates are ${y_1 = 2at_1}$ and ${y_2 = 2at_2}$.The point of intersection of the tangents at $P$ and $Q$ is given by $(at_1t_2, a(t_1 + t_2))$.Therefore,the ordinate of the intersection point is ${y_3 = a(t_1 + t_2)}$.Substituting $t_1 = \frac{y_1}{2a}$ and $t_2 = \frac{y_2}{2a}$ into the expression for $y_3$:${y_3 = a \left( \frac{y_1}{2a} + \frac{y_2}{2a} \right) = \frac{y_1 + y_2}{2}}$.This implies that $2y_3 = y_1 + y_2$,which means ${y_1, y_3, y_2}$ are in $A.P.$

If ${y_1}$ and ${y_2}$ are the ordinates of two points $P$ and $Q$ on the parabola ${y^2 = 4ax}$ and ${y_3}$ is the ordinate of the point of intersection of the tangents at $P$ and $Q$,then:

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