The equation, `2x^2+ 3y^2-8x-18y+35= K` represents (a) no locus if ` k gt 0` (b) an ellipse if ` k lt 0` (c) a point if ` k = 0` (d) a hyperbola if `k gt0`

Options

A. no locus if k gt 0
B. an ellipse if k lt 0
C. a point if k = 0
D. a hyperbola if k gt0

Answer

C

Explanation

We have
`2x^(2)+3y^(2)-8x-18y+35=k`
`"or "2(2x^(2)-4x)+3(y^(2)-6y)+35=k`
`"or "2(x-2)^(2)+3(y-3)^(2)=k`
For k = 0, we get
`2(x-2)^(2)+3(y-3)^(2)=0`
which represents the point (2, 3)