Write the standard form of the equation of the circle that passes through the points (30, -2), (-1, -19) and (-18, 12). Find the center and the radius. I don't know how to do these! Please help :)

Question

whpalmer4 · Answer

Okay, you have 3 points you know to be on the circle, and the standard formula for a circle has 3 constants (2 for the position of the center, 1 for the length of the radius) to be determined.  Your lucky day — 3 points will determine the 3 unknown constants :-)

$$(x-h)^2 + (y-k)^2 = r^2$$is the standard formula for a circle with radius $r$ and center at $(h,k)$

Plug each of your 3 known points into that equation, to get an equation in terms of $x,y,r$.  I'll do the first one:

$(30,-2)$:
$$(30-h)^2 + (-2-k)^2 = r^2$$expanding that, we get$$h^2-60h + k^2 +4k +904= r^2$$

Now do that for the other two points.  You'll end up with 3 equations in 3 unknowns, and you can solve the system of equations for the 3 unknowns.  Each of the equations will have $r^2$ as the right hand side, so I suggest you use that to help you solve them.

anonymous · Answer

Ok, makes sense! Thank you!

whpalmer4 · Answer

Happy to check your answer when you have one.