The curve represented by the equations

x = 3(cost + sint)

y = 4(cost - sint) is

Concept:

1. Equation of circle x2 + y2 = r2

2. Equation of an ellipse 

3. Equation of Parabola y2 = 4ax, x2 = 4ay

4. Equation of hyperbola 

5.If a2 = b2 then hyperbola is called rectangular hyperbola and x2 − y2 = a2 is the general form of a rectangular hyperbola

Calculation:

Given:

x = 3(cost + sint)

y = 4(cost - sint) 

 ----(1)

 ----(2)

Adding r=equation 1 and 2;

Hence, the given curve represents an ellipse.