﻿ The circle x2 + y2 – 4x – 4y + 4 = 0 is inscribed in a triangle which has two of its sides along the co-ordinate axes. The locus of the circumcentre of the triangle is x + y – xy + k(x2 + y2)1/2 = 0. Find k. : Kaysons Education

# The Circle x2 + y2 – 4x – 4y + 4 = 0 Is Inscribed In A Triangle Which Has Two Of Its Sides Along The Co-ordinate Axes. The Locus Of The Circumcentre Of The Triangle Is x + y – xy + k(x2 + y2)1/2 = 0. Find k.

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## Question

### Solution

Correct option is

1

The given circle is x2 + y2 – 4x – 4y + 4 = 0. This can be re-written as (x– 2)2 + (y – 2)2 = 4 which has centre C (2, 2) and radius 2.

Let the equation of third side is

Length of perpendicular from (2, 2) on AB = radius = CM

∴

Since origin and (2, 2) lie on the same side of AB

Hence AB is the diameter of the circle passing through âˆ†OAB, mid point of AB is the centre of the circle i.e.,

Substituting the values of a and b in (1) then

∴ Locus of (hk) is

x + y – xy +

Hence the required value of k is 1.

#### SIMILAR QUESTIONS

Q1

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Q2

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Q4

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Q7

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Q8

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Q9

Let 1 and C2 be two circles with C2 lying inside C1. A circle C lying inside C1 touches C1 internally and C2 externally. Identify the locus of the centre of C.

Q10

Tangents TP and TQ are drawn from a point T to the circle x2 + y2 = a2. If the point T lies on the line px + qy = r, find the locus of centre of the circumcircle of triangle TPQ.