Question

The general form of the equation of a circle is x^2+y^2−8x+6y+21=0.

Answer 1

Answer:

The coordinates of the center of the circle are (4,-3).

Step-by-step explanation:

The general form of the equation of a circle is

$x^2+y^2-8x+6y+21=0$

It can be written as

$(x^2-8x)+(y^2+6y)+21=0$

Add and subtract $(\frac{-b}{2a})^2$ in each parenthesis, to make perfect squares.

For first parenthesis,

$(\frac{-b}{2a})^2=(frac{8}{2(1)})^2=(4)^2=16$

For second parenthesis,

$(\frac{-b}{2a})^2=(frac{-6}{2(1)})^2=(-3)^2=9$

$(x^2-8x+16-16)+(y^2+6y+9-9)+21=0$

$(x^2-8x+16)+(y^2+6y+9)+21-16-9=0$

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

$(x-4)^2+(y+3)^2=4$                  .... (1)

The standard form of a circle is

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

Where, (h,k) is center of the circle and r is radius.

On comparing (1) and (2) we get,

$h=4,k=-3,r=2$

Therefore the coordinates of the center of the circle are (4,-3).

Answer 2

The anwser is (4,-3)