Question

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

• A. no locus if K < 0
• B. an ellipse if K < 0
• C. a point if K = 0 .
• D. a hyperbola if K > 0.

Answer 1

Answer: (C)

Given curve can be written as
$2\left(x^2-4x\right)+3\left(y^2-6y\right)+35=k$
$\Rightarrow 2\left[{\left(x-2\right)}^2-4\right]+3\left[{\left(y-3\right)}^2-9\right]+35=k$
$\Rightarrow 2{\left(x-2\right)}^2+3{\left(y-3\right)}^2=k$
For $k=0$, we get $2{\left(x-2\right)}^2+3{\left(y-3\right)}^2=0$
$\Rightarrow x=2,y=3$ i.e., the point $\left(2,3\right)$