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Maths-

General

Easy

Question

If y₁, y₂ are the ordinates of two points P and Q on the parabola and y₃ is the ordinate of the point of intersection of tangents at P and Q, then

y₁, y₂, y₃ are in A.P.
y₁, y₃, y₂ are in A.P.
y₁, y₂, y₃ are in G.P.
y₁, y₃, y₂ are in G.P.

The correct answer is: y₁, y₃, y₂ are in A.P.

P(x₁, y₁) Q(x₂, y₂)
Point of intersection of P and Q.
(x₃, y₃) = $open parentheses square root of x subscript 1 end subscript x subscript 2 end subscript end root comma fraction numerator y subscript 1 end subscript plus y subscript 2 end subscript over denominator 2 end fraction close parentheses$
$therefore$ y₃ = $fraction numerator y subscript 1 end subscript plus y subscript 2 end subscript over denominator 2 end fraction$ $rightwards double arrow$ y₁, y₃, y₂ are in A.P.

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