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Consider the curve x=1-3t^(2),y=t-3t^(2)...

Consider the curve `x=1-3t^(2),y=t-3t^(2)`. If tangent at point `(1-3t^(2),t-3t^(2))` inclined at an angle `theta` to the positive x-axis and another tangent at P(2,-3) cuts the cuve again at Q.
The value of `tan theta+ sec theta ` is equal to-

A

`3t`

B

`t`

C

`t-t^(2)`

D

`t^(2)-2t`

Text Solution

Verified by Experts

The correct Answer is:
a
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Knowledge Check

  • Consider the curve x=1-3t^(2),y=t-3t^(2) . If tangent at point (1-3t^(2),t-3t^(2)) inclined at an angle theta to the positive x-axis and another tangent at P(2,-3) cuts the cuve again at Q. The point Q will be-

    A
    `(1,-2)`
    B
    `((-1)/(3),-(2)/(3))`
    C
    `(-2,1)`
    D
    `(0,0)`

  • Consider the curve x=1-3t^(2),y=t-3t^(2) . If tangent at point (1-3t^(2),t-3t^(2)) inclined at an angle theta to the positive x-axis and another tangent at P(2,-3) cuts the cuve again at Q. The angle between the tangent at P and Q will be-

    A
    `(pi)/(4)`
    B
    `(pi)/(6)`
    C
    `(pi)/(2)`
    D
    `(pi)/(3)`

  • The curve x=1-3t^(2), y=t-3t^(3) is symmetrical with respect to -

    A
    both axes
    B
    y-axis
    C
    x-axis
    D
    none of these

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