Question

If (−4, 11) and (−6, 5) are the endpoints of a diameter of a circle, what is the equation of the circle?

A) (x + 5)^2 + (y − 8)^2 = 100
B) (x + 5)^2 + (y − 8)^2 = 10
C) (x − 5)^2 − (y + 8)^2 = 10
D) (x − 5)^2 + (y + 10)^2 = 8

Answer 1

Answer:

A. $(x+5)^2+(y-8)^2=100$

Step-by-step explanation:

1. The standard form of the equation of a circle is $(x-h)^{2} + (y-k)^2=r^2$

2. To find the center we require the  midpoint   of the  2 given points

center =$[\frac{1}{2}(-4-6),\frac{1}{2}(11+5)]$

=(-5,8)

3. The radius is the distance from the centre to either of  the 2 given points calculate the radius using the  distance formula

d= $\sqrt{(x_{2}+x_{1})^{2} +(y_{2}-y_{1})^{2}$

let $(x_{1},y_{1})= (-5,8)$ and $(x_2,y_2)=(-4,11)$

r=$\sqrt{(-4+5)^2+(11-8)^2} =\sqrt{81+9}=10$

--> $(x-(-5)^2+(y-8)^2=10^2$

--> $(x+5)^2+(y-8)^2=100$

Answer 2

Answer:

The anser is B 100% willing to put $100 on it.

Step-by-step explanation: