what is the standard form for 2x2+2y2-20x-12y+50

Question

directions: convert the general form of the equation into standard form.

Answer 1

This expression (not an equation) can be written in a similar way to an equation for a circle:

2(x²-10x)+2(y²-6y)+50, then complete the squares:

2(x²-10x+25)+2(y²-6y+9)+50-50-18,

2(x-5)²+2(y-3)²-18.

As it stands the original expression is already standard form.

But if this expression equals zero then 2(x-5)²+2(y-3)²-18=0,

(x-5)²+(y-3)²=9 which is the equation of a circle centre (5,3) and radius 3.

It's likely that the intended meaning of the question is to standardise the equation:

2x²+2y²-20x-12y+50=0 which would be the equation of a circle (see above).