Question

What is the equation of the circle with center (1, −1) that passes through the point (5, 7)?

Answer 1

Answer:

Option C $(x-1)^2+(y+1)^2=80$

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance from the center of the circle to any point on the circumference of the circle is equal to the radius of the circle

we have

(1,-1) and (5,7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute the values

$d=\sqrt{(7+1)^{2}+(5-1)^{2}}$

$d=\sqrt{(8)^{2}+(4)^{2}}$

$d=\sqrt{80}\ units$

step 2

Find the equation of the circle in center radius form

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

where

(h,k) is the center

r is the radius

substitute

$(x-1)^2+(y+1)^2=(\sqrt{80})^2$

$(x-1)^2+(y+1)^2=80$