Question

What is an equation of a circle whose center is (1, 4) and diameter is 10?

Answer 1

Answer: For Regent takers !

x^2 + 2x +y^2 +8y =8

Explanation:

Equation of a circle with center (h,k) = (x-h)^2 + (y-k)^2 = r^2

~The Center is (h,k) = (1,4)

~The Radius is diameter/2

~The diameter is 10; radius = 10/2 = 5

Steps:

~ (x-1)^2+(y-4)^2=5^2 : fill in the equation

~ x(x-2) + y(y-8) = 25 : simplify the exponents

~ x^2+2x+y^2+8y = 8 : factoring

Answer 2

Equation of a circle with center (h,k) = (x-h)^2 + (y-k)^2 = r^2
Center (h,k) = (1,4)
Radius = diameter/2
Since diameter = 10; radius = 10/2 = 5

Equation of the circle = (x-1)^2 + (y-4)^2 = 5^2
:. (x-1)^2 + (y-4)^2 = 25.
The should be the answer because if you break it down, you still have to use “completing the square” to put it back again.
Or this could also be the answer: x(x-2) + y(y-8) = 8
This is when I broke it down completely and factorized.