Question

$(3,2)$ 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

Ellipse : $16x^2+9y^2-16x-32=0$

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

Putting point (3,2) in S we get

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

$=144+36-48-32$

$=180-80$

$=100$

$S(3,2)>0$

Hence, point lies outside ellipse.