Answer for college algebra problem??

Question

Find the standard form for the equation for the circle with the following properties: Center (4,9), passes through (9,0).

I’m having a hard time figuring out the steps to make this into standard form..

Answer 1

To find center radius form you need to determine the radius of the circle, which is the distance from the given center (4,9) to the given point on the circle (9,0). Use the distance formula.

R = √(9-4)²+(9-0)² = √25+81 = √106

So center radius form is (x-4)²+(y-9)² = 106

To get to standard form square each binomial, combine similar terms (subtracting 106 from both sides):

x²-8x+16 + y²-18y+81=106

You should be able to take it from there.

Answer 2

We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.

Let's find the r^2:

Center (4,9), passes through (9,0)

(h,k) (x,y)

(9-4)^2 + (0-9)^2 = r^2

(5)^2 + (-9)^2 = r^2

106 = r^2

Thus, the equation of the circle is:

(x-4)^2 + (y-9)^2 = 106

I hope this helps :)