Question

The position of the point (1,3)n with respect to the ellipse $4x^2+9y^2-16x-54y+61=0$ is

• A. Outside the ellipse
• B. On the ellipse
• C. On the major axis
• D. On the minor axis

Answer 1

The correct option is A Outside the ellipse

We have,

Equation of given ellipse,

$4x^2+9y^2-16x-54y+61=0$

Given point,

Let, $(x,y)=(1,3)$

Then, position of point in given ellipse is

$4{\left(1\right)}^2+9{\left(3\right)}^2-16\left(1\right)-54\left(3\right)+61=0$

$\Rightarrow 4+81-16-162+61=0$

$\Rightarrow 146-178=0$

$\Rightarrow -32<0$

The position of point outside the ellipse.