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tia_tia [17]
3 years ago
9

Which equation represents the circle described? (in picture)

Mathematics
1 answer:
Sedaia [141]3 years ago
6 0
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=\dfrac{8x}{2x}=4\implies x^2-8x+4^2\\\\\\y^2-6y+b^2\implies b=\dfrac{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).
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