Home
Class 12
MATHS
Prove that the chord y-xsqrt(2)+4asqrt(2...

Prove that the chord `y-xsqrt(2)+4asqrt(2)=0` is a normal chord of the parabola `y^2=4a x` . Also find the point on the parabola when the given chord is normal to the parabola.

Text Solution

Verified by Experts

The correct Answer is:
`(2a,-2sqrt(2)a)`
Equation of normal to the parabola `y^(2)=4ax` having slope m is
`y=mx-2an-am^(3)`
Comparing this equation with `y=sqrt(2)x-4asqrt(2)`, we get `m=sqrt(2)`
`and" "2am+am^(3)=2sqrt(2)a+2sqrt(2)a=4asqrt(2)`
Thus, given on the parabola is `(am^(2),-2am)-=(2a,-2sqrt(2)a)`.
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

Prove that the chord y-x sqrt(2)+4a sqrt(2)=0 is a normal chord of the parabola y^(2)=4ax . Also find the point on the parabola when the given chord is normal to the parabola.

Prove that the chord y-xsqrt2+4asqrt2=0 is a normal chord of the parabola y^2=4ax . Also, find the point on the parabola when the given chord is normal to the parabola.

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

The normal chord of the parabola y^(2)=4ax subtends a right angle at the vertex.Then the length of chord is

The normal chord of the parabola y^(2)=4ax subtends a right angle at the focus.Then the end point of the chord is

If the normal chord of the parabola y^(2)=4 x makes an angle 45^(@) with the axis of the parabola, then its length, is

Find the locus of midpoint normal chord of the parabola y^(2)=4ax

PQ is normal chord of the parabola y^(2)=4ax at P(at^(2),2at) .Then the axis of the parabola divides bar(PQ) in the ratio

A normal chord of the parabola y^(2)=4ax subtends a right angle at the vertex if its slope is