Vertical

Vertical problem:(vertical definition)

A ) 4
B ) 1
C ) 2
D ) 0
E ) 3
Steps to derive
1 x = t3 - 3t, y = 3t2 - 9
[Write the parametric equations.]
2 dxdt = 3t2 - 3, dydt = 6t
[Find dxdt and dydt.]
3 At points where dxdt = 0 but dydt ≠ 0, the tangent is vertical.
4 dydt ≠ 0, 6t ≠ 0, t ≠ 0
5 3t2-3 = 0
[Equate dxdt to zero.]
6 t = ± 1
[Solve for t.]
7 At t = 1, x = - 2 and y = - 6
[Find x, y at t = 1.]
8 At t = - 1, x = 2 and y = - 6
[Find x, y at t = -1.]
9 The coordinates of the points at which the tangent is vertical are (- 2 , - 6) and (2, - 6).
10 So, there's four vertical tangents for the given parametric curve.


Hence the right answer is Option C

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