First slide

Definition of a circle

Question

For all values of a, equation of a diameter
of the circle $x^{2} + y^{2} - 2 a x + 2 a y + a^{2} = 0$ is

Moderate

A

$x + y = a$
B

$x - y = a$
C

$x + y = 2 a$
D

$x - y = 2 a$

Solution

Centre of the circle is $(a, - a)$ and the line $x - y = 2 a$ passes through it. So it is a diameter of the given circle.

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