Question

The point on the ellipse $x^2+2y^2=6$ whose distance from the line $x+y=7$ is least is:

• A. $(1,2)$
• B. $(-2,1)$
• C. $(1,-2)$
• D. $(2,1)$

Answer 1

Answer: (D)

$(2,1)$

Given equation of ellipse $\frac{x^2}{6}+\frac{y^2}{3}=1$

Slope of the tangent at any point $P(x_1,y_1)$ to

$\frac{x^2}{6}+\frac{y^2}{3}=1$ is given by

$2x+4y\frac{dy}{dx}=0$$\Rightarrow x=2y$

Putting $x=2y$ in the equation of ellipse we have $y=1$.

Evidently the point lies in the first quadrant

$\therefore y=1$ and $x=2$.