Question

The graph ($y$ vs $x$) represented by $x={\sin }^{2}t,y=2\cos t$ is

• A. Parabola
• B. Portion of parabola
• C. part of sine graph
• D. Part of Hyperbola

Answer 1

The correct option is A Parabola

Given, $x={\sin }^{2}t$

$x=1-{\cos }^{2}t$ and

and $y=2\cos t$

Thus $\frac{y}{2}=\cos t$.

Substitution in the equation of $x$ gives us

$x=1-{\left(\frac{y}{2}\right)}^2$

$4x=4-y^2$

$y^2=4(1-x)$

$y^2=-4(x-1)$.

This represents a parabola.