find a cartesian equation for the parabola given in parametric form by the equations
x= t-1, y = t^2 +t
b) prove that the point (at^2, 2at) always lies on the curve with equation y^2 = 4ax. state the value of t at the point:
(a, -2a)
Parabola(Pure matsh)
2007-02-09 5:10 am
回答 (1)
2007-02-09 5:26 am
✔ 最佳答案
(a)x = t - 1
y = t² + t
So, y = (x+1)² + (x+1)
= x² + 3x + 2
Part (b) follows...
2007-02-08 21:30:31 補充：
(b)Put (at², 2at) into y² = 4ax:RHS = 4a(at²) = (2at)² = LHSSo, (at², 2at) is a point on y² = 4ax, for any real number t.(at², 2at) = (a, -2a)i.e. at² = a and 2at = -2ai.e. t = ±1 and t = -1So, t = -1.
2007-02-08 21:30:43 補充：
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