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If y=2x+3 is a tangent to the parabola y...

If `y=2x+3` is a tangent to the parabola `y^2=24 x ,` then find its distance from the parallel normal.

Text Solution

Verified by Experts

The correct Answer is:
`(75)/(sqrt(5))`
The equation of normal to the parabola `y^(2)=24x` having slope m is `y=mx-12m-6m^(3)`.
It is parallel to y=2x+3. Therefore, m=2.
Then the equation of the parallel normal is
y=2x-24-48=2x-72
The distance between y=2x+3 and y=2x-72 is
`|(72+3)/(sqrt(4+1))|=(75)/(sqrt(5))`
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