A curve has parametric equations:
x = 2 + t2 y = 4t
Find the cartesian equation of this curve.
A cartesian equation of a curve is simply finding the single equation of this curve in a standard form where xs and ys are the only variables.
To find this equation, you need to solve the parametric equations simultaneously:
If y = 4t, then divide both sides by 4 to find (1/4)y = t.
This newly found value of t can be substituted into the equation for x:
x = 2 + (1/4(y))2 - expand the bracket (square both 1/4 and y) to derive x = 2 + 1/16 y2.
Technically, this final equation is already in cartesian form as it only includes variables x and y, however to further rearrange the equation to find the standard 'y =' form:
x = 2 + 1/16 y2 (minus 2 from both sides)
x - 2 = 1/16 y2 (multiply each side by 16)
16x - 32 = y2 (and finally take square roots of both sides)
y = SQRT(16x-32)