Question

Which of the following points is an exterior point of the ellipse $16x^2+9y^2-16x-32=0$.

• A. $(\frac{1}{2},2)$
• B. $(\frac{1}{4},2)$
• C. $(3,2)$
• D. none of these

Answer 1

Answer: (B), (C)

The correct options are
B $(\frac{1}{4},2)$
C $(3,2)$

Let $S=16x^2+9y^2-16x-32$
Now $S(\frac{1}{2},2)=4+36-8-32=0\Rightarrow$ point on the ellipse.
$S(\frac{1}{4},2)=1+36-4-32>0\Rightarrow$ point is exterior to the ellipse.
$S(3,2)=144+36-48-32>0\Rightarrow$ point is exterior to the ellipse.