Question

The coordinates of the point on the ellipse $16x^2+9y^2=400$ where the ordinate decrease at the same rate at which the abscissa increases, are

• A. $(3,\frac{16}{3})$
• B. $(-3,\frac{16}{3})$
• C. $(3,\frac{-16}{3})$
• D. $(3,-3)$

Answer 1

The correct option is A $(3,\frac{16}{3})$

Equation of ellipse $16x^2+9y^2=400$

$\Rightarrow 32x\frac{dx}{dt}+18y\frac{dy}{dt}=0$

$\Rightarrow (32x-18y)\frac{dx}{dt}=0$

$\Rightarrow x=\frac{9}{16}y$

Using this in equation of ellipse ,

$\Rightarrow 225y^2=6400$

$\Rightarrow y=\frac{16}{3}$

$\Rightarrow x=3$