Question

Write the standard equation for the circle that passes through the points (1, 1), (1, 3), and (9, 2).

So I know d=-79 but I dont' know e or f

Answer 1

General equation is\[x^2 + y^2 + dx + ey + f = 0\]

first equation is
\[-2 = d + e + f\]

Second equation is\[-10 = d + 3e + f\]

third equation is
\[-85 = 9d + 2e +f\]

Answer 2

First minus second gave me e=-4

second minus third gave me \[75 = -8d + e\]

e=-4 minus the other gave me \[d=-79/8\]

Answer 3

But x & y are multiplied by 8 so then d would then be -79. But what would that make e? -4/8 = -1/2. But I tried that answer and it did not work

Answer 4

I know that in order to find f I need to find d & e, which I know the answer to d (-79) but not e

Answer 5

Its cool that your using equations to solve for it (like a boss), but just graph the points. From there, you can easily figure out the radius and center. Once you have that, plug it into the equation (x-h)^2 + (y-k)^2 = r^2

Where h is the x component of the center, k is the y component and r^2 is the radius squared. From there, factor everything out and you have your answer

Answer 6

Haha thanks. But I just called my teacher (I'm homeschooled) to see if I could use that way on a test. He said no.. So I have to figure out how to do it his way.. Haha which wouldn't be so bad until you get to the super tricky ones.