The point (3,4) is on a circle with center (1,4). Write the standard equation of the circle
Mathematics · Middle School · Tue Nov 03 2020
Answered on
The standard equation of the circle is (x-h)^2+(y-k)^2=r^2
Given the center of the circle at (1,4)
(x-1)^2 + (y-4)^2 = r^2
To determine the value of r or the radius we simply subtract the Center X to Point X, in this case
3 - 1 = 2
Radius is R^2 which means that 2^2 = 4
(x-1)^2 + (y-4)^2 = 4
simplifying it further, we expand the values of x and y inside the parenthesis
x^2 - 2x + 1 + y^2 - 8y + 16 = 4
x^2 + y^2 - 2x - 8y + 17 - 4 = 0
Standard equation : x^2 + y^2 - 2x - 8y + 13 = 0
Check:
(x^2 - 2x + __) + (y^2 - 8y + __ ) = -13
Find the values that would make the would make the equation factorable inside the parenthesis, and whatever number is added inside the parenthesis will also be added in the right side of the equation.
(x^2 - 2x + 1 ) + (y^2 - 8y + 16 ) = -13 + 1 + 16
(x-1)^2 + (y-4)^2 = 4