Question

Write the equation of a circle with center (6,4) that passes through the coordinate (2,1). In your final answer, include all of your calculations.

Answer 1

All points along the circle with be the distance of the radius from the center...so the radius can be found using the Pythagorean Theorem..

r^2=(4-1)^2+(6-2)^2

r^2=9+16

r^2=25

r=5

The equation of the circle can be expressed as:

r^2=(x-h)^2+(y-k)^2 where (h,k) correspond to the center of the circle, (2,1) in this case.

(x-2)^2+(y-1)^2=25

if you wanted it in a more standard form...

(y-1)^2=25-(x-2)^2

(y-1)^2=25-x^2+4x-4

(y-1)^2=-x^2+4x+21

y-1=(-x^2+4x+21)^(1/2)

y=1(+/-)(-x^2+4x+21)^(1/2)

Answer 2

Answer:

(X - 6)^2 - (y - 4)^2 = 25

Step-by-step explanation:

Same as what shown except the center is (6,4 not (2,1)