Answer to Question #114122 in Analytic Geometry for Randal Rodriguez

Question

Find the area of the circle whose equation is x2
+ y2
= 6x – 8y.

Answer 1

$x^2+y^2=6\times x-8\times y;\\x^2+y^2-6\times x+8\times y=0;\\x^2-6\times x+y^2+8\times y=0;\\(x^2-6\times x+9)+(y^2+8\times y+16)=25;\\(x-3)^2+(y+4)^2=5^2;\\R=5;S=\pi\times R^2;\\S=3.14\times25=78.5\,units\, squared;$

Answer: the area of the circle is 78.5 units squared.