Question

The standard form of the equation of a circle is (x−4)2+(y−2)2=9. What is the general form of the equation?

x2+y2+8x+4y−29=0

x2+y2−8x−4y−29=0

x2+y2−8x−4y+11=0

x2+y2+8x+4y+11=0

Answer 1

`x^(2)+y^(2)-8x-4y+11=0`

Explanation:

we have

`(x-4)^(2)+(y-2)^(2)=9`

The general equation of the circle is equal to

`x^(2)+y^(2)+Ax+By+C=0`

Convert the standard form to a general form

`(x-4)^(2)+(y-2)^(2)=9\\ \\(x^(2) -8x+16)+(y^(2)-4y+4)=9\\ \\x^(2)+y^(2)-8x-4y+20-9=0\\ \\x^(2)+y^(2)-8x-4y+11=0`