Question

Write the standard equation for the circle that passes through the points:

(0, 0)

(6, 0)

(0, - 8)

Answer 1

For my first equation I got f=0 because \[0^2 + 0^2 + 0d + 0e +f =0\]

Then for my second equation I got \[-36=6d+f\]

For my third equation I got \[-64=-8e\]

The problem I have now is that I have to subtract my second equation from my first equation, but the first equation isn't really an equation I don't think. It's just zero. So would I just turn \[-36 = 6d + f ...into... 36 = -6d - f\]

Answer 2

Write the standard equation for the circle that passes through the points:
(0, 0)
(6, 0)
(0, - 8)
Standard form of equation for a circle: (x-h)^2+(y-k)^2=r^2, (h,k) being the (x,y) coordinates of the center, r=radius.
Solving for h, k and r, using given points
..
Equation for point (0,0):
(0-h)^2+(0-k)^2=r^2
eq1) h^2+k^2=r^2
..
Equation for point (6,0):
(6-h)^2+(0-k)^2=r^2
eq2) (6-h)^2+k^2=r^2
..
Equation for point (0,-8):
(0-h)^2+(-8-k)^2=r^2
eq3) h^2+(-8-k)^2=r^2
..
eq1) h^2+k^2=r^2
eq2) (6-h)^2+k^2=r^2


subtract eq2 from eq1 eliminating k^2 and r^2
h^2-(6-h)^2=0
h^2-(36-12h+h^2)=0
h^2-36+12h-h^2=0
12h=36
h=3
..
eq1) h^2+k^2=r^2
eq3) h^2+(-8-k)^2=r^2
subtract eq3 from eq1 eliminating h^2 and r^2
k^2-(-8-k)^2=0
k^2-(64+16k+k^2)=0
k^2-64-16k-k^2=0
-16k=64
k=-4
..
eq1) h^2+k^2=r^2
3^2+(-4)^2=r^2
9+16=r^2
r^2=25
..
Equation of given circle:
(x-3)^2+(y+4)^2=25

Answer 3

Well I was given the equation \[x^2 + y^2 + dx + ey + f = 0\] to use

Answer 4

It's the same equation, just distribute it out. x-3 squared is x^2 -6x + 9

y+4 squared is y^2 + 8y + 16

All together, in your form, the equation would be:

x^2 + y^2 -6x + 8y + 9 + 16 - 25 = 0

Answer 5

That would be my final equation?

Answer 6

simply the constants, which in this case would be zero. If your ever unsure, graph the points. From a quick sketch, you can find the radius and center. From there, you can use the equation Nurali used, then just work out the algebra like I did to find the other form. Try it now on some scratch paper to see if you know what I'm saying. It should take you like a minute tops

Answer 7

Oh okay. Yeah graphing always helps. Thanks!!