Home
Class 12
MATHS
Find the equation of the chord of the pa...

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.

Text Solution

Verified by Experts

Let `M(4,y_(1))` be midpoint of the chord. So, equation of chord using equation `T=S_(1)` is
`yy_(1)-4(x+4)=y_(1)^(2)-8xx4`
`or" "yy_(1)-4x=y_(1)^(2)-16`
Slope `=(4)/(y_(1))=2` (Given)
`:." "y_(1)=2`
So, equation of the chord is
2y-4x=-12
y=2x-6
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.8|1 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.9|2 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 5.6|1 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 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 to the parabola y^2=8x having slope 2 and also find the point of contact.

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

The length of the common chord of the parabolas y^(2)=x and x^(2)=y is

Find the equation of the tangents to the parabola 3y^(2)=8x , parallel to the line x-3y=0 .

The point of intersection of the tangents of the parabola y^2=4x drawn at the endpoints of the chord x+y=2 lies on (a) x-2y=0 (b) x+2y=0 (c) y-x=0 (d) x+y=0

Length of the shortest normal chord of the parabola y^2=4ax is

Find the equation of normal to the parabola y^(2)=4x , paralle to the straight line y=2x .

Find the locus of the midpoint of normal chord of parabola y^2=4a xdot

Find the equation of the tangent to the parabola y^(2)=8x at the point (2t^(2),4t) . Hence find the equation of the tangnet to this parabola, perpendicular to x+2y+7=0