The equation of an ellipse with its major axis along the (y )-axis is ( x^ 2 9 + y^ 2…

MATHEMATICS · Subjective · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

The equation of an ellipse with its major axis along the

y

-axis is

\dfrac{x^{2}}{9}+\dfrac{y^{2}}{16}=1

. A point

Q

moves such that its coordinates are given by

Q(t,\,t-1)

, where

t\in\mathbb{R}

. (a) Obtain the condition on

t

for which the point

Q

lies inside the ellipse. (b) Find the value(s) of

t

for which

Q

lies exactly on the ellipse. (c) Determine the set of all real

t

for which the point

Q

lies outside the ellipse.