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If (x_1, y_1) and (x_2, y_2) and ends of a focal chord of the

Question

If $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ and ends of a focal chord of the parabola $y^{2} = 4 a x$ , then square of G.M. of $x_{1}$ and $x_{2}$ is?

- 4 a^{2}

4 a^{2}

a^{2}

- a^{2}

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Liam Discussed

(x_{1}, y_{1})

and

(x_{2}, y_{2})

and ends of a focal chord of the parabola

y^{2} = 4 a x

, then square of G.M. of

x_{1}

and

x_{2}

is?

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Parabola:

y^{2} = 4 a x

Let

(x_{1}, y_{1}) = (a t^{2}, 2 a t)

(x_{2}, y_{2})

is another end of focal chord of the Parabola.

∴ (x_{2}, y_{2}) = (\frac{a}{t ^{2}}, \frac{- 2 a}{t})

Square of GM of

x_{1}

and

x_{2}

= (a t^{2} \times \frac{a}{t ^{2}})^{2} = a^{2}

Hence the GM of

x_{1}

and

x_{2}

a^{2}

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Question Text	If $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ and ends of a focal chord of the parabola $y^{2} = 4 a x$ , then square of G.M. of $x_{1}$ and $x_{2}$ is?
Answer Type	Text solution:1
Upvotes	150