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sarumanplaysguitar
 The equation of a circle with center [tex](8,7)[/tex] and radius [tex]9[/tex] is as follows:

[tex](x-8)^2+(y-7)^2=9^2[/tex]

Multiplying this equation out will give us the general form of the equation of the circle.

[tex](x-8)^2+(y-7)^2=9^2 \\ (x-8)(x-8)+(y-7)(y-7)=81 \\ (x^2-16x+64) + (y^2 -14x + 49) = 81 \\ x^2-16x+64 + y^2 -14x + 49 = 81[/tex]

Simplify to get your answer:

[tex]x^2+y^2 -16x-14y + (49+64) = 81 \\ x^2+y^2 -16x-14y + 113 = 81[/tex]
mathmate
This question has been answered before by someone else.
If the answer provided did not suit your teacher/computer, it might be that the standard form is required, which is the first line of the previous response:

Equation of circle centred at (a,b) with radius r is:
(x-a)^2+(y-b)^2=r^2

with (a,b)=(8,7), i.e. a=8, b=7,  and r=9, the equation of the circle becomes

(x-8)^2+(y-7)^2=9^2
OR
(x-8)^2+(y-7)^2=81

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