Question

The equation of $2x^2+3y^2-8x-18y+35=k$ represents

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Given equation, $2x^2+3y^2-8x-18y+35-k=0$
Compare with $a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$, we get
a=2, b=3, h=0, g=-4, f=-9, c=35-k
$△=abc+2fgh-a{f}^2-b{g}^2-c{h}^2$
=6(35-k)+0-162-48-0
$△$=210-6k-210=-6k; $△$=0, If k=0
So, that given equation is a point if k=0.