First slide

Definition of a circle

Question

The normal at the point (3, 4) on a circle at the point (-1,-2). The equation of the circle, is

Moderate

A

$x^{2} + y^{2} + 2 x - 2 y - 13 = 0$
B

$x^{2} + y^{2} - 2 x - 2 y - 11 = 0$
C

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

$x^{2} + y^{2} - 2 x - 2 y + 14 = 0$

Solution

The normal at $P (3, 4)$ cuts the circle again at $Q (- 1, - 2)$ . Therefore, PQ is a diameter of the circle. Hence, its equation is
$(x - 3) (x + 1) + (y - 4) (y + 2) = 0$
or $x^{2} + y^{2} - 2 x - 2 y - 11 = 0$

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