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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 angel `theta` with the positive direction of x-axis is

A

`y = x tan theta - 2 cot theta`

B

`x = y cot theta + 2 tan theta`

C

`y = x tan theta + 2 cot theta`

D

`x = y cot theta - 2 tan theta`

Text Solution

Verified by Experts

The correct Answer is:
B
Given parabola is `x^(2) = 8y`
Now, slope os tangent at any point (x,y) on the parabola (i) is
`(dy)/(dx) = (x)/(4) = tan theta`
[`:'` tangent is making an angle `theta` with the positive direction of X-axis]
So, `x = 4 tan theta`
`implies y = 2 tan^(2) theta`
Now, equation of requried tangent is
`y - 2 tan^(2) theta = tan theta (x - 4 tan theta)`
`implies y = x tan theta - 2 tan^(2) theta implies x = y cot theta + 2 tan theta`
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