Question

If the endpoints of the diameter of a circle are (9, 4) and (5, 2), what is the standard form equation of the circle?

A) (x + 7)2 + (y + 3)2 = 5
B) (x − 7)2 + (y − 3)2 = 5
C) (x + 7)2 + (y + 3)2 = 5
D) (x − 7)2 + (y − 3)2 = 5

Answer 1

The believe the answer is (x − 7)2 + (y − 3)2 = 5.

Answer 2

The correct option is D.

Explanation:

The endpoints of the diameter of a circle are (9, 4) and (5, 2).

The midpoint of these end points is circle.

`C=((9+5)/(2),(4+2)/(2))=(7,3)`

The center of the circle is (7,3).

The length of diameter is

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`d=√((9-5)^2+(2-4)^2)`

`d=√(20)`

`d=2√(5)`

The radius of the circle is

`r=(d)/(2)=(2√(5))/(2)=√(5)`

The general equation of the circle is

`(x-h)^2+(y-k)^2=r^2`

`(x-7)^2+(y-3)^2=(√(5))^2`

`(x-7)^2+(y-3)^2=5`

Therefore correct option is D.