﻿ The locus of the foot of the perpendicular drawn from the centre of the ellipse  on any tangent is  : Kaysons Education

# The Locus Of The Foot Of The Perpendicular Drawn From The Centre Of The Ellipse  on Any Tangent Is

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## Question

### Solution

Correct option is

Let P(hk) be the foot of the perpendicular drawn from the centre C(0, 0) of the ellipse to any tangent

Then,

Since CP is perpendicular to the tangent given in (i).

Substituting the value of m in (ii), we get

Hence, the locus of P(hk) is

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#### SIMILAR QUESTIONS

Q1

Let S(3, 4) and S(9, 12) be two foci of an ellipse. If the coordinates of the foot of the perpendicular from focus S to a tangent to the ellipse is (1, –4), then the eccentricity of the ellipse is

Q2

Let S and S’ be two foci of the ellipse . If a circle described on SS’ as diameter intersects the ellipse in real and distinct points, then the eccentricity e of the ellipse satisfies

Q3

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Q4

If PSQ is a focal chord of the ellipse 16x2 + 25y2 = 400 such that SP = 8, then SQ =

Q5

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Q6

Tangent at a point on the ellipse  is drawn which cuts the coordinates axes at A and B. The minimum area of the triangleOAB is (O being origin)

Q7

The locus of the foot of the perpendicular from the foci on any tangent to the ellipse

Q8

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Q9

The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is

Q10

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