﻿ The tangent at any point P of the hyperbola  makes an intercept of length p between the point of contact and the transverse axis of the hyperbola, p1, p2 are the lengths of the perpendiculars drawn from the foci on the normal at P, then : Kaysons Education

# The Tangent At Any Point P of The Hyperbola  makes An Intercept Of Length p between The Point Of Contact And The Transverse Axis Of The Hyperbola, p1, p2 are The Lengths Of The Perpendiculars Drawn From The Foci On The Normal At P, Then

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## Question

### Solution

Correct option is

P is a harmonic mean between p1 and p2

Let F1(ae, 0) and F2(–ae, 0) be the foci of the hyperbola.

Equation of the tangent at normal at P are

is the point of intersection of the tangent at P and the x-axis.

is point where the normal at P meets x-axis.

From

Similarly

.

#### SIMILAR QUESTIONS

Q1

If F1 = (3, 0), F2 = (–3, 0) and P is any point on the curve 16x2 +25y2 = 400, then PF1 + PF2 equal

Q2

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Q3

The normal at an end of a latus rectum of the ellipse  passes through an end of the minor axis if

Q4

If an ellipse slides between two perpendicular straight line, then the locus of its center is

Q5

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Q6

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse. x2 + 9y2 = 9, meets the auxillary circle at the point M, then the area of the triangle with vertices at A, M and the origin is

Q7

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.

Q8

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Q9

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Q10

The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola y2 = 8x, is