MyQuestionIcon

4

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Theorems for Differentiability

Middle point ...

Question

Middle point of the chord of the parabola $y^{2} = 4 a x$ which pass through a given point (p, q)

Open in App

Solution

Let P(h, k) be the mid point of chord of parabola $y^{2} = 4 a x$
so equation of chord is $y k - 2 a (x + h) = k^{2} - 4 a h$ Since it passes through $(p, q)$
$∴ q k - 2 a (p + h) = k^{2} - 4 a h$ $∴$ Required locus is $y^{2} - 2 a x - q y + 2 a p = 0$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The locus of the middle points of all chords of the parabola

y^{2} = 4 a x

passing through the vertex is

Q. Prove that the locus of the middle points of all chords of the parabola

y^{2} = 4 a x

passing through the vertex is the parabola

y^{2} = 2 a x

Q. Prove that the locus of the middle points of all chords of the parabola

y^{2} = 4 a x

which are drawn through the vertex is the parabola

y^{2} = 2 a x .

Q. Find the locus of the middle points of all chords of the parabola

y^{2} = 4 a x

which are drawn through the vertex.

Q. Find the locus of the middle points of chords of the parabola

y^{2} = 4 a x

which are of constant length

2 l

.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Theorems for Differentiability

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Theorems for Differentiability

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon