Question

Find the equation of a circle with a center of(5, 7) where a point on the circle is (10, 19)

Answer 1

(x - 5)² + (y - 7)² = 169

Explanation:

The standard form of the equation of a circle 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) = (5, 7), thus

(x - 5)² + (y - 7)² = r²

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

Calculate the radius using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (5, 7) and (x₂, y₂ ) = (10, 19)

r =
`√((10-5)^2+(19-7)^2)`

=
`√(5^2+12^2)`

=
`√(25+144)` =
`√(169)` = 13, hence

(x - 5)² + (y - 7)² = 169 ← equation of circle