First slide

Definition of a circle

Question

If a circle has two of its diameters along the lines
$x + y = 5$ and $x - y = 1$ and has area $9 π,$ then the equation of the circle
is

Moderate

A

$x^{2} + y^{2} - 6 x - 4 y + 4 = 0$
B

$x^{2} + y^{2} - 6 x - 4 y - 3 = 0$
C

$x^{2} + y^{2} - 6 x - 4 y - 4 = 0$
D

$x^{2} + y^{2} - 6 x - 4 y + 3 = 0$

Solution

Two diameters $x + y = 5$ and $x - y = 1$ intersect at
(3, 2) which is the centre of the circle. Let $r$ be the radius of the
circle. Then,
Area $= 9 π \Rightarrow π r^{2} = 9 π \Rightarrow r = 3$ .
So, the equation of the circle is
$(x - 3)^{2} + (y - 2)^{2} = 3^{2}$ or, $x^{2} + y^{2} - 6 x - 4 y + 4 = 0$

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