Question

The equation $2x^2+3y^2-8x-18y+35=\lambda$ represents?

• A. A circle for all $\lambda$
• B. An ellipse if $\lambda <0$
• C. The empty set if $\lambda >0$
• D. A-point if $\lambda =0$

Answer 1

The correct option is D A-point if $\lambda =0$

Given:

$2x^2+3y-8x-18y+35=\lambda$

$2(x^2-4x)+3(y^2-6y+35)=\lambda$

$2{(x-2)}^2+3{(y-3)}^2=\lambda$

For $\lambda =0$, then

$2{(x-2)}^2+3{(y-3)}^2=0$

Thus, the point is $(2,3)$.

Hence, the correct option is ‘d’.