First slide

Definition of a circle

Question

The length of the tangent from (0, 0) to the circle
$2 (x^{2} + y^{2}) + x - y + 5 = 0$ is

Moderate

A

$\sqrt{5}$
B

$\sqrt{5} / 2$
C

$\sqrt{2}$
D

$\sqrt{5 / 2}$

Solution

The equation of the circle can be written as
$x^{2} + y^{2} + \frac{1}{2} x - \frac{1}{2} y + \frac{5}{2} = 0$
Let $I$ be the length of tangent drawn from (0, 0) to the given circle. Then,
$l = \sqrt{S_{1}} = \sqrt{0 + 0 + 0 - 0 + \frac{5}{2}} = \sqrt{\frac{5}{2}}$

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