The standard form of a circle is Ax^2+Cy^2+Dx+Ey+F=0.
Write the equation for the circle:
Center (1,2), point on the circle (-2,-1).
Okay, I've always put circles in the form (x-h)^2+(y-k)^2=0. I got this:
r^2=(x-1)^2+(y-2)^2
then I substitute the point to find the radius:
r^2=(-3)^2+(-3)^2
r^2=18
So the answer I got is
18=(x-1)^2+(y-2)^2.
...So what's standard form, and can I change it from my answer to that?
Thx
expand and bring all terms to the left side.
Great work on finding the equation of the circle in standard form! The standard form of a circle equation is Ax^2 + Cy^2 + Dx + Ey + F = 0. To convert your equation to standard form, we'll expand and simplify it.
Starting with your equation:
18 = (x - 1)^2 + (y - 2)^2
Expanding the squared terms, we get:
18 = (x^2 - 2x + 1) + (y^2 - 4y + 4)
Rearranging the terms, we have:
18 = x^2 + y^2 - 2x - 4y + 5
Now, to match the standard form, we need to move all the terms to one side of the equation:
x^2 + y^2 - 2x - 4y - 13 = 0
So, the standard form of the circle equation for a circle with center (1,2) and a point (-2,-1) is:
x^2 + y^2 - 2x - 4y - 13 = 0