Question

write the standard equation: 2x^2+2y^2+4x-28y+86=0

Answer 1

is it a circle, parabola ,hyperbola or a ellipse?

Answer 2

coefficient of the \(x^2\) term is the same as the coefficient of the \(y^2\) term
this tells you it is a circle

Answer 3

unless it is a point, or nothing

Answer 4

Step 1 : Divide the whole equation by 2 to make the coefficient of x^2 & y^2 =1 (That will standardize the equation)

Step 2: Check for equality of coefficients of x^2 & y^2 if they are equal & coifficient of term xy is zero then it is a circle (Which is the case here .