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Parametric Equation of Tangent

If y1,y2 are ...

Question

If $y_{1}, y_{2}$ are the ordinates of two points P and Q on the parabola and $y_{3}$ is the ordinate of the point of intersection of tangents at P and Q, then

A

y_{1}, y_{2}, y_{3}

are in A.P

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B

y_{1}, y_{3}, y_{2}

are in A.P

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C

y_{1}, y_{2}, y_{3}

are in G.P

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D

y_{1}, y_{3}, y_{2}

are in G.P

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Solution

The correct option is B $y_{1}, y_{3}, y_{2}$ are in A.P
Let $y_{1} = 2 a t_{1}, y_{2} = 2 a t_{2}, t h e n y_{3} = a (t_{1} + t_{2})$
$y_{3} = a (t_{1} + t_{2}) = \frac{2 a t_{1} + 2 a t_{2}}{2} = \frac{y_{1} + y_{2}}{2} . ∴ y_{1}, y_{3}, y_{2} a r e i n A . P$

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