First slide

Definition of a circle

Question

Equation of the circle with centre on the y-axis and passing through the origin and the point (2, 3) is

Moderate

A

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

$3 x^{2} + 3 y^{2} + 13 x + 3 = 0$
C

$6 x^{2} + 6 y^{2} - 13 x = 0$
D

$3 x^{2} + 3 y^{2} - 13 y = 0$

Solution

$Let center = C (0, k)$
$\begin{array}{l} Circle passes through O (0, 0) and A (2, 3) \\ O C^{2} = A C^{2} \Rightarrow k = 13 / 6 \end{array}$
$Radius = 13 / 6$
$Equation of the required circle is 3 x^{2} + 3 y^{2} - 13 y = 0$

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