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

Answer:

The correct option is D.

Step-by-step explanation:

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

The midpoint of these end points is circle.

$C=(\frac{9+5}{2},\frac{4+2}{2})=(7,3)$

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

The length of diameter is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$d=\sqrt{(9-5)^2+(2-4)^2}$

$d=\sqrt{20}$

$d=2\sqrt{5}$

The radius of the circle is

$r=\frac{d}{2}=\frac{2\sqrt{5}}{2}=\sqrt{5}$

The general equation of the circle is

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

$(x-7)^2+(y-3)^2=(\sqrt{5})^2$

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

Therefore correct option is D.