At how many points do the following curves intersect: \frac{y^2}{9}-\frac{x^2}{16}=1 and \frac{x^2}{4}+\frac{(y-4)^2}{16}=1

NIMCET 2024 Paper

Section: Mathematics

Question : 16 of 120

Marks: +1, -0

At how many points do the following curves intersect:

\;{y^2}/{9}-\;{x^2}/{16}=1

and

\;{x^2}/{4}+\;{(y-4)^2}/{16}=1

Solution:

The axis of hyperbola lies along

y

axis and major axis of the ellipse also lies on

y

axis. Centre of the ellipse is

(0,4)

and length of its major axis is 8 . Thus, it passes through origin.

Hence there will be only two intersection points.

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