Question

Find the equation of the circle with center (10, 0) and point (5, 2).

Answer 1

(x - 10)² + y² = 29

Explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (10, 0), thus

(x - 10)² + (y - 0)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (10, 0) and (x₂, y₂ ) = (5, 2)

r =
`√((5-10)^2+(2-0)^2)`

=
`√((-5)^2+2^2)`

=
`√(25+4)` =
`√(29)`

Thus

(x - 10)² + (y - 0)² = (
`√(29)` )², that is

(x - 10)² + y² = 29 ← equation of circle