Eliminate the parameter t and expressy explicitly in terms o

Eliminate the parameter t and expressy explicitly in terms of x for the equations 2t 1-12 Select one: .

Solution

Let

t = tan(z)

Then

x = (1 - tan²z)/(1 + tan²z) = cos2z

and

y = 2tan(z)/( 1 + tan²z) = sin2z

Now

x^2 + y^2 = (cos2z)^2 + (sin2z)^2 = 1

y = ±sqrt(1 - x^2) (Option d is correct)