First slide

Definition of a circle

Question

Tangents AB and AC are drawn to the circle $x^{2} + y^{2} - 4 x - 6 y + 2 = 0$ from $A (- 3, - 2)$ . Then equation of circle passing through A, B and C is

Moderate

A

$x^{2} + y^{2} + x + y - 12 = 0$
B

$x^{2} + y^{2} + x + y + 12 = 0$
C

$x^{2} + y^{2} + x - y - 12 = 0$
D

$x^{2} + y^{2} - x + y - 12 = 0$

Solution

$x^{2} + y^{2} - 4 x - 6 y + 2 = 0$
Centre D= (2, 3)
Clearly AD is the diameter of the circle passing through A, B, C
(x+3) (x-2) + ( y+2) (y-3) = 0
$\Rightarrow x^{2} + y^{2} + x - y - 12 = 0$

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