Mathematics: The equation of a circle x^2 + y^2 + 6y=7. what are the coordinates of the center and the length of the radius of the circle? a) center (0,3) and radius 4 b) center (0,-3) and radius 4 c) center (0,3) and radius 16 d) center (0,-3) and radius 16

I think it is 1/2 i hope it works...

The equation of a circle x^2 + y^2 + 6y=7. what are

sarahsteelman

15.01.2022

Option B) center (0,-3) and radius

Step-by-step explanation:

we know that

The equation of the circle into center radius form is equal to

$(x-h)^{2}+(y-k)^{2}=r^{2}$

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

$x^{2} +y^{2}+6y=7$

convert to center radius form

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} +(y^{2}+6y+9)=7+9$

$x^{2} +(y^{2}+6y+9)=16$

Rewrite as perfect squares

$x^{2} +(y+3)^{2}=16$

$x^{2} +(y+3)^{2}=4^{2}$

The center is the point (0,-3)

The radius is units

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