Question

What is the standard form of this equation of `x^ { 2} + y ^ { 2} + 14x - 4y - 28= 0`?

Answer 1

`(x+7)^2+(y-2)^2=81`

Explanation:

`"using the method of "color(blue)"completing the square"`

`"collect the x and y terms together"`

`x^2+14x+y^2-4y=28`

`rArr(x+7)^2+(y-2)^2=28color(red)(+49+4)`

`rArr(x+7)^2+(y-2)^2=81larr" in standard form"`

`"this is the equation of a circle with"`

`"centre "=(-7,2)" and radius "=9`
graph{((x+7)^2+(y-2)^2-81)=0 [-40, 40, -20, 20]}