Question

Which equation represents the circle described? (in picture)

I'm not sure I believe its C or D

Answer 1

You are right. In circle equation we have =r² so the correct answer will be C od D. But we have to calculate the center of a circle.


`x^2+y^2-8x-6y+24=0\quad|-24\\\\(x^2-8x)+(y^2-6y)=-24`

Complete the square:


`x^2-8x+a^2\implies a=(8x)/(2x)=4\implies x^2-8x+4^2\\\\\\y^2-6y+b^2\implies b=(6y)/(2y)=3\implies y^2-6y+3^2`

And we have:


`(x^2-8x)+(y^2-6y)=-24\\\\(x^2-8x+4^2)-4^2+(y^2-6y+3^2)-3^2=-24\\\\ (x-4)^2+(y-3)^2-16-9=-24\\\\(x-4)^2+(y-3)^2-25=-24\quad|+25\\\\\boxed{(x-4)^2+(y-3)^2=1}`

So the answer is C (the same left side of equation).