Question

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The general form of the equation of a circle is x2 + y2 + 8x + 22y + 37 = 0.
The equation of this circle in standard form is (x + )2 + (y + )2 =
. The center of the circle is at the point ( , ).

Answer 1

Answer:

(-4,-11)

Step-by-step explanation:

Given an equation of a circle

$x^{2} +y^{2} +8x+22y+37 =0$

To find the centre and radius of the circle.

We group x terms to gether and y terms to gether first.

$x^{2}  +8x+y^{2}+22y+37 =0$

Now completion of squares method is used for both x and y.

$x^{2}  +8x+16-16+y^{2}+22y+121-121+37 =0$

$(x+4)^{2}  +(y+11)^{2}-100 =0$

$(x+4)^{2}  +(y+11)^{2} =10^{2}$

Thus we find that the centre = (-4,-11) and radius

= 10