Find a rectangular equation for the plane curve defined by t

Find a rectangular equation for the plane curve defined by the parametric equations. x = 5 cos t, y = -2 sin t; 0 lessthanorequalto t lessthanorequalto 2 pi 4x^2 - 25y^2 = 100; x greaterthanorequalto 5 4x^2 +25y^2 = 1; -1/5 lessthanorequalto x lessthanorequalto y 4x^2 - 25y^2 = 1; x greaterthanorequalto 1/2 4x^2 +25y^2 = 100; -5 lessthanorequalto x lessthanorequalto 5

Solution

x = 5cost, y = -2sint

=> 2x = 10cost and 5y = -10sint

Squarting and adding

4x^2 + 25y^2 = 100[cos^2.t + sin^2.t)

4x^2 + 25y^2 = 100 (since cos^2.t + sin^2.t = 1)

When t lies between 0 to 2.pi, then x lies between -5 and 5

Hence answer is D.