Question

Find the equation of a circle
passing through the origin, radius 17 and ordinate of the centre is −15.

Answer 1

Let (h, k) be the centre of a circle with radius a.
Thus, its equation will be

\[\left( x - h \right)^2 + \left( y - k \right)^2 = a^2\]

Let the required equation of the circle be

\[\left( x - h \right)^2 + \left( y - k \right)^2 = a^2\]

Given:
k = −15, a = 17
The circle passes through the point (0, 0).
∴ Equation of the circle:

\[\left( 0 - h \right)^2 + \left( 0 - 15 \right)^2 = \left( 17 \right)^2\]

⇒ \[h = \pm 8\]

Hence, the required equation of the circle is

\[\left( x - 8 \right)^2 + \left( y + 15 \right)^2 = {17}^2\]  or

\[\left( x + 8 \right)^2 + \left( y + 15 \right)^2 = {17}^2\]

\[x^2 + y^2 \pm 16x + 30y = 0\]