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The equation of a tangent to the parabol...

The equation of a tangent to the parabola, `x^(2) = 8y`, which makes an angle `theta` with the positive direction of x-axis, is:

A

`y=x tan theta + 2cot theta`

B

`y=x tan theta + 2tan theta`

C

`x = y cot theta + 2 tan theta`

D

`y = x tan theta - 2 cot theta`

Text Solution

Verified by Experts

The correct Answer is:
C
`x^(2) = 7y` at `(x^(1), y^(1))`
`2x_(1) = 8 (dy)/(dx) = 8tan theta, x_(1) = 4 tan theta`
Also `x_(1)^(2) = 8y_(1) rArr 16 tan^(2) theta = 8y_(1) rArr y_(1) = 2 tan^(2) theta`
Equation of tangent by T = 0
`x x_(1) = 4(y + y_(1)) " " (4 tan theta) x = 4(y + 2 tan^(2) theta)" " x = y cot theta + 2 tan theta`
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