Question

1.

The center of circle P is at (1, 1). Point B(-1, 3) is on the circle. Write the
equation of circle P.

Answer 1

(x - 1)² + (y - 1)² = 8

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 ) = (1, 1 ) and r has to be found

the radius r is the distance from the centre to any point on the circle

calculate r using the distance formula

r =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = P (1, 1 ) and (x₂, y₂ ) = B (- 1, 3 )

r =
`√((-1-1)^2+(3-1)^2)`

=
`√((-2)^2+2^2)`

=
`√(4+4)`

=
`√(8)`

then equation of circle is

(x - 1 )² + (y - 1)² = (
`√(8)` )² , that is

(x - 1)² + (y - 1)² = 8