Home
Class 12
MATHS
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))`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise 5.7|9 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Single)|98 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.5|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

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

If y=2x+3 is a tangent to the parabola y^(2)=24x, then is distance from the parallel normal is 5sqrt(5)(b)10sqrt(5)(c)15sqrt(5)(d) None of these

If 2y=x+24 is a tangent to a parabola y^(2)=24x, then its distance from the parallel normal is

if y=4x+3 is parallel to a tangent to the parabola y^2=12x , then its distance from the normal parallel to the given line is

If y=2x-3 is a tangent to the parabola y^(2)=4a(x-(1)/(3)) then 'a' is equal to:

If the line y=2x+k tangent to the parabola y=x^(2)+3x+5 then find 'k' is

The line y=mx+c is a tangent to y^(2)=4mx ,then distance of this tangent from the parallel normal is

If y=2x-3 is a tangent to the parabola y^(2)=4a(x-(1)/(3)) then the value of |a| is

y=2x+3 is a Tangent to the parabola y^(2)=4a(x-(1)/(3)) then 3(a-5)=