Question

Find the equations of the circles passing through two points on Y-axis at distances 3 from the origin and having radius 5.

Answer 1

Let the required equation of the circle be ${\left(x-h\right)}^2+{\left(y-k\right)}^2=a^2$.

The circle passes through the points (0, 3) and (0, −3).

∴ ${\left(0-h\right)}^2+{\left(3-k\right)}^2=a^2$ ...(1)
And, ${\left(0-h\right)}^2+{\left(-3-k\right)}^2=a^2$ ...(2)

Solving (1) and (2), we get:
k=0

Given:
Radius = 5
∴ a² = 25

So, from equation (2), we have:
$h^2+9=25\Rightarrow h=\pm 4$

Hence, the required equation is ${\left(x\pm 4\right)}^2+y^2=25$, which can be rewritten as $x^2\pm 8x+y^2-9=0$.