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

• A

  outside the ellipse
• B

  on the ellipse
• C

  on the minor axis
• Correct answer
  D

  on the major axis

Solution

Given, equation of ellipse is $$ 4 x^2+9 y^2-16 x-54 y+61=0 $$ It can be written as, $$ \frac{(x-2)^2}{9}+\frac{(y-3)^2}{4}=1 $$ Centre of ellipse $(2,3)$. vertex are $(5,3),(-1,3)$ Focus are $(2+\sqrt{5}, 3),(2-\sqrt{5}, 3)$
$\therefore(1,3)$ lies on major axis.

Hence, the correct answer is option: 'D'.