Home
Class 12
MATHS
Find the equation of the tangent to the ...

Find the equation of the tangent to the parabola `y^2=8x` having slope 2 and also find the point of contact.

Text Solution

Verified by Experts

The equation of the tnagent to `y^(2)=4ax` having slope m is `y=mx+(a)/(m)`
Hence, for the given parabola, the equation of the tangent is
`y=2x+(2)/(2)ory=2x+1`
and the point of contact is
`((a)/(m^(2)),(2a)/(m))-=((2)/(2^(2)),(2(2))/(2))-=((1)/(2),2)`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise 5.1|11 Videos
  • PARABOLA

    CENGAGE|Exercise Exercise 5.2|17 Videos
  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos
  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|4 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the tangent to the parabola x=y^2+3y+2 having slope 1.

Find the equation of the tangent at t =2 to the parabola y^(2) = 8x .

Find the equation of the tangent to the parabola y=x^2-2x+3 at point (2, 3).

The equation of the directrix of the parabola y^(2)=-8x is

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

Find the equations of the tangent and normal to the parabola y^(2)=8x at t=1/2

Find the equations of the tangent: to the parabola y^(2)=16x , parallel to 3x-2y+5=0

Find the equation of the chord of the parabola y^(2)=8x having slope 2 if midpoint of the chord lies on the line x=4.

Find the equation of the common tangent to the curves y^2=8x and xy=-1.

Find the equation of normal to the hyperbola 3x^2-y^2=1 having slope 1/3dot