First slide

Definition of a circle

Question

Given that the circles $x^{2} + y^{2} - 2 x + 6 y + 6 = 0$ and $x^{2} + y^{2} - 5 x + 6 y + 15 = 0$ touch, the equation to their common tangent, is

Moderate

A

$x = 3$
B

$y = 6$
C

$7 x - 12 y - 21 = 0$
D

$7 x + 12 y + 21 = 0$

Solution

Using $S_{1} - S_{2} = 0$ WC obtain $3 x - 9 = 0 or, x = 3$ as the equation of the required common tangent

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