Square of length of tangent drawn from point (α ,β ) to circle a{x^2} + a{y^2} = {r^2} is

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10-1.Circle and System of Circles

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Square of the length of the tangent drawn from the point $(\alpha ,\beta )$ to the circle $a{x^2} + a{y^2} = {r^2}$ is

A

$a{\alpha ^2} + a{\beta ^2} - {r^2}$

B

${\alpha ^2} + {\beta ^2} - \frac{{{r^2}}}{a}$

C

${\alpha ^2} + {\beta ^2} + \frac{{{r^2}}}{a}$

D

${\alpha ^2} + {\beta ^2} - {r^2}$

Solution

(b) Length of tangent is $\sqrt {{S_1}} $.

Equation of circle is ${x^2} + {y^2} – \frac{{{r^2}}}{a} = 0$

Hence ${S_1} = {\alpha ^2} + {\beta ^2} – \frac{{{r^2}}}{a}$.

Standard 11

Mathematics

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