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  • The ordinates of the points P and Q on the parabola with focus (3.0) and directrix x=-3 are in the ratio 3 : 1 :. If R<img alt="(\alpha ,\beta )" src="https://entrancecorner.oncodecogs.com/g

The ordinates of the points P and Q on the parabola with focus (3.0) and directrix x=-3 are in the ratio 3 : 1 :.
If R(\alpha ,\beta ) is the point of intersection of the tangents to the parabola at P and Q, then\frac{\beta^2}{\alpha} is equal to

Option: 1

16


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Parabola is \mathrm{y}^2=12 \mathrm{x} Let \mathrm{Q}\left(3 \mathrm{t}^2, 6 \mathrm{t}\right) so \mathrm{P}\left(27 \mathrm{t}^2, 18 \mathrm{t}\right) \begin{aligned} & \mathrm{R}(\alpha, \beta)=\left(\mathrm{at}_1 \mathrm{t}_2, \mathrm{a}\left(\mathrm{t}_1+\mathrm{t}_2\right)\right) \\ & =(3 \mathrm{t} \cdot 3 \mathrm{t}, 3(\mathrm{t}+3 \mathrm{t})) \\ & \mathrm{R}(\alpha, \beta)=\left(9 \mathrm{t}^2, 12 \mathrm{t}\right) \\ & \frac{\beta^2}{\alpha}=\frac{(12 t)^2}{9 t^2}=\frac{144}{9}=16 \\ & \end{aligned}

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Ritika Kankaria

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