still need help with this parameter equation

Question

The ellipse (x^2/9^2)+(y^2/5^2)=1 can be drawn with parametric equations where x(t) is written in the form: x(t)=rcos(t) with r= __?___

and y(t)=__?__

Answer 1

This ellipse is the collection of all points (x,y) such that x² /81 + y²/25 = 1

r is the distance from (x,y) to the origin (0,0)

t is the angle r makes with the x-axis

think of t as short for theta, the usual Greek letter for an angle

x(t)= rcost

y(t)= rsint

r ²= x²+y² for a circle, but for this ellipse 25x² + 81y² = 25(81)= 2025

or 25rcost + 81rsint =2025

factor out the r

r(25cost+81sint) = 2025

r = 2025/(25cost+81sint)