﻿ Find the locus of middle points of chords of the circle x2 + y2 = a2, which subtend right angle at the point (c, 0). : Kaysons Education

# Find The Locus Of Middle Points Of Chords Of The Circle x2 + y2 = a2, Which Subtend Right Angle At The Point (c, 0).

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## Question

### Solution

Correct option is

2(x2 + y2) – 2cx + c2 – a2 = 0

Let N (hk) be the middle point of any chord AB, which subtend a right angle at P(c, 0).

(since distance of the vertices from middle point of the hypotenuse are equal)

or

∴ Locus of N(hk) is

2(x2 + y2) – 2cx + c2 – a2 = 0

#### SIMILAR QUESTIONS

Q1

Find the length of the tangents drawn from the point (3, – 4) to the circle 2x2 + 2y2 – 7x – 9y – 13 = 0.

Q2

Find the area of the triangle formed by tangents from the point (4, 3) to the circle x2 + y2 = 9 and the line segment joining their points of contact is

Q3

Find the length of the tangent from any point on the circle x2 + y2 + 2gx+ 2fy + c = 0 to the circle x2 + y2 + 2gx + 2fy + c1 = 0 is

Q4

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Q5

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Q6

Find the condition that chord of contact of any external point

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Q7

The chord of contact of tangents drawn from a point on the circle x2 +y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 = y2 = c2. Show that abc are in GP.

Q8

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Q9

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Q10

Find the equations of the tangents from the point A(3, 2) to the circle x2y2 + 4x + 6y + 8 = 0 .