Question

Question 10

The point (-3, 6) is on a circle with a center at (2,3). What is the equation of the circle?

Answer 1

( x - 2)^2 + ( y - 3)^2 = 34

Explanation:

The equation of the circle with a center and a point

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

( a, b) - the center of the circle

( x, y) - any point on the circle

r^2 - radius of the circle

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

x = -3

y = 6

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

a = 2

b = 3

Step 1: substitute the center into the equation

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

Step 2: sub the point into the equation

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

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

( -5)^2 + 3^2 = r^2

25 + 9 = r^2

34 = r^2

Step 3: sub the radius into the equation

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

( x - 2)^2 + ( y - 3)^2 = 34

Therefore, the equation of the circle is

( x - 2)^2 + ( y - 3)^2 = 34