Equations of tangents drawn from origin to circle {x^2} + {y^2} - 2rx - 2hy + {h^2} = 0 are

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10-1.Circle and System of Circles

hard

The equations of the tangents drawn from the origin to the circle ${x^2} + {y^2} - 2rx - 2hy + {h^2} = 0$ are

A

$x = 0,y = 0$

B

$({h^2} - {r^2})x - 2rhy = 0,x = 0$

C

$y = 0,x = 4$

D

$({h^2} - {r^2})x + 2rhy = 0,x = 0$

(IIT-1988)

Solution

(b) The equation of tangents is $S{S_1} = {T^2}$

$ \Rightarrow {h^2}({x^2} + {y^2} – 2rx – 2hy + {h^2})$

$= {(rx + hy – {h^2})^2}$

$\Rightarrow ({h^2} – {r^2}){x^2} – 2rhxy = 0 $

$\Rightarrow x\{ ({h^2} – {r^2})x – 2rhy\} = 0$

$ \Rightarrow x = 0,\;({h^2} – {r^2})x – 2rhy = 0$.

Standard 11

Mathematics

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