Question

PLZ HELP ASAP FEATURES OF A CIRLE FROM EXPANDED EQUATION

Answer 1

First we need to convert the given equation to standard form, only then we can find the center and radius of the circle.

$x^{2} + y^{2} +18x+14y+105=0 \\ \\ x^{2} +18x+ y^{2}+14y=-105 \\ \\ x^{2} +2(x)(9)+ y^{2}+2(y)(7)=-105 \\ \\ x^{2} +2(x)(9)+ 9^{2} + [y^{2}+2(y)(7)+7^{2}] =-105+9^{2}+7^{2} \\ \\ (x+9)^{2}+ (y+7)^{2}=25$

The standard equation of circle is:

$(x-a)^{2} + (y-b)^{2}= r^{2}$

with center (a,b) and radius = r

Comparing our equation to above equation, we can write

Center of circle is (-9, -7) and radius of the given circle is 5