First slide

Definition of a circle

Question

f the tangent at the point P on the circle $x^{2} + y^{2} + 6 x + 6 y = 2$ meets the straight line $5 x - 2 y + 6 = 0$ at a point $Q$ on the y-axis, then the length of $P Q,$ is

Moderate

A

4
B

$2 \sqrt{5}$
C

5
D

$3 \sqrt{5}$

Solution

The line $5 x - 2 y + 6 = 0$ cuts y-axis at $at Q (0, 3) .$
Clearly, $P Q$ is the length of the tangent drawn from $Q$ on the circle
$x^{2} + y^{2} + 6 x + 6 y - 2 = 0$
$∴ P Q = \sqrt{0 + 9 + 6 \times 0 + 6 \times \bar{3 - 2}} = 5$

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