Conic section question

Geometry Level 3

What curve is represented by following equation.

x 2 4 − y 2 4 ( sin ⁡ 2 t − 1 ) = 1 \dfrac{x^2}{ 4} - \dfrac{y^2}{4(\sin^2 t - 1)} = 1

Details : t t does not belong to n π 2 \dfrac{n\pi}{2} .

Ellipse Parabola Pair of straight line Hyperbola

Subh Mandal by subh mandal , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Subh Mandal
Jan 19, 2016

Take -1 common from the 2nd part of equation. To get (x^2÷4)+(y^2÷(4×(1-sin^2(t))))=1 So comparing b^2=a^2 (1-e^2) We get e=|sin t| which is always less than 1 and greater than 0 in the specified set of value of t. Therefore curve is ellipse. Or we could replace sin^2 (t)-1 by -cos^2t to get a standard ellipse equation.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...