Question

The endpoints of a

diameter of a circle are (2,
4) and (-4, 7). What is the
standard form of the
equation
of this circle?

I know one of the answer is not c

Hurry i got like 30 mins left and a girl is tired

Answer 1

2nd option

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 is at the midpoint of the endpoints of the diameter.

The coordinates of the centre is the average of the coordinates of the endpoints.

centre = (
`(-4+2)/(2)`,
`(7-1)/(2)` ) = (
`(-2)/(2)` ,
`(6)/(2)` ) = (- 1, 3 )

the radius is the distance from the centre to either of the endpoints

using the distance formula to calculate r

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

with (x₁, y₁ ) = (- 1, 3 ) and (x₂, y₂ ) = (2, - 1 )

r =
`√((2-(-1))^2+(-1-3)^2)`

=
`√((2+1)^2+(-4)^2)`

=
`√(3^2+16)`

=
`√(9+16)`

=
`√(25)`

= 5

then equation of circle is

(x - (- 1) )² + (y - 3)² = 5² , that is

(x + 1)² + (y - 3)² = 25