Question

Write the equation of each circle.
35. center at (-3,-3), passes through (-2,3)

Answer 1

(x + 3)² + (y + 3)² = 37

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.

we have the centre and require r

the radius is the distance from the centre to a 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 ) = (- 3, - 3 ) and (x₂, y₂ ) = (- 2, 3 )

r =
`√((-2-(-3))^2+(3-(-3))^2)`

=
`√((-2+3)^2+(3+3)^2)`

=
`√(1^2+6^2)`

=
`√(1+36)`

=
`√(37)`

then equation of circle is

(x - (- 3))² + (y - (- 3))² = (
`√(37)` )² , that is

(x + 3)² + (y + 3)² = 37