Question

How to find paramatric equation for a given curve?
Anyone who can help me finding the paramatric equation of the curve x^(2/3) + y^(2/3) = a^(2/3)

Answer 1

to find the parametric equation of the curve, u need to find x any y separately as the function of a....x=f(a),y=f(a).....such that the above equation satisfies.
for this equation,we use the fact that sint^2 + cost ^2 =1
so my substitution will be x=a (cost)^3
y=a(sint)^3
(because i saw the power of 2/3 in x,when i needed 2)
if u put these ,u will get RHS as a^2/3
so the parametric equations are
x=a (cost)^3
y=a (sint)^3

Answer 2

got it @vishwajeet

Answer 3

@hartnn thanks! Would you please do a favour of doing the same for a parabola and a hyperbola!

Answer 4

there are various equations for parabola and hyperbola
the parametric substitution will depend on the equation...
if u give an equation,then i can tell u specific substitution for it...

Answer 5

@hartnn y^2 = 4x +5 and (x^2)/16 - (y^2)/9 = 1

Answer 6

for parabola, u can put x=t^2-5/4,(so that 4x becomes,4t-5...to eliminate constant 5).,then u get y as 2t(y^2=4*t^2).....
for hyperbola,are u familiar with hyperbolic functions sinh x,cosh x?