First slide

Definition of a circle

Question

The equations of the tangents drawn from the origin to the circle
$x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0$ , is

Moderate

A

$x = 0, y = 0$
B

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

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

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

Solution

The combined equation of the pair of tangents drawn from $(x_{1}, y_{1})$ to a circle $S = 0$ is given by $S S' = T^{2} .$
So, the equations of the tangents drawn from $(0, 0)$ to
$x^{2} + y^{2} - 2 r x - 2 h y + h^{2} = 0 a$ are given by
$h^{2} (x^{2} + y^{2} - 2 r x - 2 h y + h^{2}) = {(- x r - h y + h^{2})}^{2}$
$\Rightarrow x \{(h^{2} - r^{2}) x - 2 r h y\} = 0$
$\Rightarrow x = 0$ or $(h^{2} - r^{2}) x - 2 rhy = 0$

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