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Does anyone know how to solve this??

Does anyone know how to solve this??-example-1
User Fatboy
by
4.5k points

1 Answer

5 votes

Answer:

(x - 3)² + (y + 1)² = 65

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

The centre C is at the midpoint of the endpoints of the diameter.

Using the midpoint formula to find C

C = (
(7-1)/(2),
(6-8)/(2) ) = (
(6)/(2),
(-2)/(2) ) = (3, - 1 )

The radius is the distance from the centre to either of the endpoints of the diameter.

Using the distance formula to find r

with C (3, - 1 ) and (7, 6 ) , then

r =
√((7-3)^2+(6+1)^2)

=
√(4^2+7^2)

=
√(16+49)

=
√(65)

Then equation of circle is

(x - 3)² + (y - (- 1) )² = (
√(65) )², that is

(x - 3)² + (y + 1)² = 65 ← equation of circle

User Quincy
by
5.0k points