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 $\left(2, 3\right)$