Question

Which is the equation of a circle that has a center of (-1, 3) and passes through the point (3, 6)?

Answer 1

Answer:

( x + 1)^2 + ( y - 3)^2 = 25

Step-by-step explanation:

The equation of the circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( a , b) - center of the circle

( x , y) - any point on the circle

r^2 - radius

( -1 , 3) - ( center) - ( a, b)

a = -1

b = 3

( 3 , 6) - ( point) - ( x, y)

x = 3

y = 6

Step 1: substitute the center into the equation

( x -(-1)^2 + ( y - 3)^2 = r^2

( x + 1)^2 + ( y - 3)^2 = r^2

Step 2: sub the point into the equation

( x + 1)^2 + (y - 3)^2 = r^2

( 3 + 1)^2 + ( 6 - 3)^2 = r^2

4^2 + 3^2 = r^2

16 + 9 = r^2

25 = r^2

Step 3: sub the radius into the equation

( x + 1)^2 + ( y - 3)^2 = r^2

( x + 1)^2 + (y - 3)^2 = 25

Therefore, the equation of the circle is

( x + 1)^2 + (y - 3)^2 = 25