Find the center (h,k) of the circle with the equation x^2+y^2-6y=7.

Question

(h,k)=(_,_)
a. 0,9
b.-3,9
c.0,3
d.9,16
Thanks for your help..........

Answer 1

Giiven equation x ^2 + y ^2 -6y = 7

To complte the squre Add (half coefficient of y )^2 to each side.

y coefficient = -6

(half coefficient of y )^2 = (-6/2)^2 = 9

So add 9 to each side.

x ^2 + y ^2 -6y + 9 = 7 + 9

x ^2 + ( y - 3 ) ^2 = 16

( x - 0 )^2 + ( y - 3 )^2 = 4^2

Compare it to standard form of circle ( x - h )^2 + ( y - k )^2 = 0.

Center ( h , k ) = (0, 3)

Option C is correct choice.

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