X^2 + y^2 +4y =3 complete the square on the x and y terms to find the radius and center of a circle

Center = (0, -4)

Radius = units

Step-by-step explanation:

We are given;

The equation of a circle;

We are required to determine the radius and the center of the circle;

To do this we are going to use completing square method;

Since we don't have the x term then;

We add the square of half the coefficients of x and y on both sides of the equation;

That is;

We get;

Taking the squares;

But we know when the equation of a circle is written in the form of;

, where (a,b) is the center and r is the radius of the circle.

Thus, in this case;

Center = (0, -4)

Radius = units

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4