Question

Write the equation of the circle graphed below

Answer 1

(x - 4)² + (y - 3)² = 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 ) = (4, 3 )

The radius r 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 ) = (- 1, 1) and (x₂, y₂ ) = (4, 3)

r =
`√((4+1)^2+(3-1)^2)`

=
`√(5^2+2^2)`

=
`√(25+4 )` =
`√(29)`

Then

(x - 4)² + (y - 3)² = (
`√(29)` )² , that is

(x - 4)² + (y - 3)² = 29 ← equation of circle

Answer 2

(x-4)² + (y-3)² =29

Explanation:

The equation of a circle is

(x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.

In this circle, the center is at (4, 3)

(x-4)² + (y-3)² = r²

and we have point (-1 ; 1)

r²=(-1-4)² + (1-3)² = 25+4=29

(x-4)² + (y-3)² =29