Question

PLZ HELP ASAP FEATURES OF A CIRCLE FROM ITS EXPANDED EQUATION

Answer 1

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


`x^(2) +y^(2) +14x-10y+65=0 \\ \\ x^(2) +2(x)(7)+ y^(2)-2(y)(5)=-65 \\ \\ x^(2) +2(x)(7)+ (7)^(2)+ [y^(2)-2(y)(5)+ (5)^(2)]=-65+(7)^(2)+(5)^(2) \\ \\ (x+7)^(2)+(y-5)^(2)=9`

The above equation is in standard form.

The center of the circle is (-7, 5) and its radius is 3.