First slide

Definition of a circle

Question

The equation $x^{2} + y^{2} - 6 x + 8 y + 25 = 0$ represents

Moderate

A

a point $(3, - 4)$
B

a pair of straight lines $x = 3, y = - 4$
C

a circle of non-zero radius
D

none of these

Solution

We have
$\begin{aligned} x^{2} + y^{2} - 6 x + 8 y + 25 = 0 \\ \Rightarrow (x - 3)^{2} + (y + 4)^{2} = 0 \\ \Rightarrow x - 3 = 0 and y + 4 = 0 \end{aligned}$
$\Rightarrow x = 3, y = - 4$ which gives the point $(3, - 4) .$

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