Find the equation of circle passing through the origin,radius 17 and ordinate of the centre is -15.
Dear Student!
Let the centre of the circle be (h, k).
Radius of the circle, r = 17
Ordinate of centre, k = – 15
Equations of the circle is
(x – h)2 + [y – (– 15)]2 = (17)2
⇒ (x – h)2 + (y + 15)2 = 289 ...(1)
Given, (0, 0) lies on (1).
∴ (0 – h)2 + (0 + 15)2 = 289
⇒ h2 + 225 = 289
⇒ h2 = 289 – 225 = 64
⇒ h = ± 8
When h = 8,
Equations of the circle is
(x – 8)2 + (y + 15)2 = 289
When h = – 8
Equations of the circle is
(x – (– 8))2 + (y + 15)2 = 289
∴ (x + 8)2 + (y + 15)2 = 289
Cheers!