Question

I just need help figuring out why what I have is wrong because yeah.
Determine the center and radius of the following circle equation: x ^2 +y^2 −14x−4y−47=0

Well I put (7,2) for center and 7 for radius.

Answer 1

Did you complete the square properly? Let me do it real quick..

Answer 2

Your center is correct. Your radius is wrong — it should be 10.

\(x^{2}+y^{2}-14x-4y-47=0\)

\((x^2-14x+\alpha)+(y^2-4y+\beta)=47+\alpha+\beta\)

Apply PST's, \(\alpha=(\frac{-14}{2})^2=49\) and \(\beta=(\frac{-4}{2})^2=4\)
\((x^2-14x+49)+(y^2-4y+4)=47+49+4\)

Condense each PST
\((x-7)^2+(y-2)^2=100\)

This is now in standard form for a circle \((x-a)^2+(y-b)^2=r^2\) where the center is (a,b) and radius is r.

By this, the center is (7,2) and the radius is 10.



Do you see your mistake now?

Answer 3

I'm thinking that you must've done a careless error or you forgot to add 49 and 4 to the other side.