Question

PLEASE HELP!!!
Eliminate the parameter. x = 5 cos t, y = 5 sin t. Answer must be a rectangular equation

Answer 1

Answer:

$x^2+y^2=25$

Step-by-step explanation:

Recall the following Pythagorean Identity:

$\sin^2(\theta)+\cos^2(\theta)=1$

Let's solve the x equation for cos(t) and the y equation for sin(t).

After the solve we will plug into our above identity.

x=5cos(t)

Divide both sides by 5:

(x/5)=cos(t)

y=5sin(t)

Divide both sides by 5:

(y/5)=sin(t)

Now we are ready to plug into the identity:

$\sin^2(t)+\cos^2(t)=1$

$(\frac{y}{5})^2+(\frac{x}{5})^2=1$

$\frac{x^2}{5^2}+\frac{y^2}{5^2}=1$

Multiply both sides by 5^2:

$x^2+y^2=5^2$

This is a circle with center (0,0) and radius 5.

All I did to get that was compare our rectangular equation we found to

$(x-h)^2+(y-k)^2=r^2$

where (h,k) is the center and r is the radius of a circle.