# Find the position of the point (1,1) relative to the ellipse $\large\frac{x^2}{64}+\frac{y^2}{100}$=1.

$\begin{array}{1 1}(a)\;\text{Outside the ellipse}\\(b)\;\text{Inside the ellipse}\\(c)\;\text{centre of the ellipse}\\(d)\;\text{None of these}\end{array}$

Given equation lof the ellipse can be written as
$100x^2+64y^2=6400$
$\Rightarrow\:100x^2+64y^2-6400=0$
Substituting the coordinates $(1,1)$ in this equation, we get
$100(1)+64(1)-6400 < 0$
Which lies outside the ellipse.
Hence (a) is the correct answer.
edited Mar 24, 2014