Question

$(2,3)$ lies _______ the ellipse $16x^2+9y^2-16x-32=0$

• A. Inside
• B. Outside
• C. On
• D. None of the above

Answer 1

The correct option is B Outside

Given ellipse $16x^2+9y^2-16x-32=0$

Let $S=16x^2+9y^2-16x-32=0$

Put $(2,3)$ in $S$ we get

$S(2,3)=16(2{)}^2+9(3{)}^2-16\left(2\right)-32=81$

$S(2,3)>0$

So it $(2,3)$ lies outside the ellipse.