Locus of points from which perpendicular tangent can be drawn to circle {x^2} + {y^2} = {a^2} , is

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10-1.Circle and System of Circles

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Locus of the points from which perpendicular tangent can be drawn to the circle ${x^2} + {y^2} = {a^2}$, is

A

A circle passing through origin

B

A circle of radius $2a$

C

A concentric circle of radius $a\sqrt 2 $

D

None of these

Solution

(c) Required locus is $S{S_1} = {T^2}$

$({x^2} + {y^2} – {a^2})({h^2} + {k^2} – {a^2}) = {(hx + ky – {a^2})^2}$

But as given, coefficient of ${x^2} + $ coefficient of ${y^2} = 0$

$ \Rightarrow $${h^2} + {k^2} = 2{a^2}$.

Hence locus of the point is the circle with centre $(0, 0)$ and radius $a\sqrt 2 $.

Standard 11

Mathematics

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