Question

Can someone please help me with this question?

Answer 1

`\large\boxed{(x-2)^2+(y+5)^2=148}`

Explanation:

The standard form of an equation of a circle:

`(x-h)^2+(y-k)^2=r^2`

(h, k) - center

r - radius

We have the center (2, -5) → h = 2 and k = -5.

Therefore the equation is:

`(x-2)^2+(y-(-5))^2=r^2\\\\(x-2)^2+(y+5)^2=r^2`

The circle passes through the point (4, 7). Put x = 4 and y = 7 to the equation:

`(4-2)^2+(7+5)^2=r^2\\\\2^2+12^2=r^2\\\\4+144=r^2\\\\r^2=148`

Finally we have:

`(x-2)^2+(y+5)^2=148`