Question

Complete the parametric equations for the given rectangular equation.

Answer 1

1) x = 5√(1-sin^2t)

2) y = = -2+3t

Explanation:

1)

Given rectangular equation:

x^2/25 + y^2 =1

Parametric equations y=-sint and x=?

Find parametric equation for x

Substituting value of y =-sint in given rectangular equation, we get

x^2/25 + (-sint )^2 =1

x^2/25 + sin^2t =1

x^2 + 25sin^2t = 25

x^2 =25 - 25sin^2t

taking square root on both sides

x= √(25 - 25sin^2t)

= √25(1-sin^2t)

= 5√(1-sin^2t)

2)

Given rectangular equation:

y=-3x+4

Parametric equations x=2-t and y=?

Find parametric equation for y

Substituting value of x=2-t in given rectangular equation, we get

y= -3(2-t) +4

= -6+3t+4

= -2+3t !