﻿ Two rods of lengths a and b slide along the x-axid and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is : Kaysons Education

# Two Rods Of Lengths a and b slide Along The x-axid And y-axis Respectively In Such A Manner That Their Ends Are Concyclic. The Locus Of The Centre Of The Circle Passing Through The End Points Is

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

4 (x2 – y2) = a2 – b2

Let C (hk) be the centre of the circle passing through the end points of the rod AB and PQ of length a and b respectively, CL and CM be perpendiculars from C on AB and PQ respectively. (Fig.)

PM = (1/2) PQ = b/2

and CA = CP (radii of the same circle)

So that locus of (hk) is 4(x2 – y2) = a2 – b2

#### SIMILAR QUESTIONS

Q1

Equation of a circle through the origin and belonging to the co-axial system, of which the limiting points are (1, 2), (4, 3) is

Q2

If a line segment AM = a moves in the plane XOY remaining parallel toOX so that the left end point A slides along the circle x2 + y2 = a2, the locus of M is

Q3

If common chord of the circle C with centre at (2, 1) and radius r and the circle x2 + y2 – 2x – 6y + 6 = 0 is a diameter of the second circle, then the value of r is

Q4

Tangents drawn from the point P(1, 8) to the circle x2 + y2 – 6x – 4y – 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle in PAB is

Q5

Let ABCD be a quadrilateral with area 18, with side AB parallel to CD and AB = 2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is

Q6

An equilateral triangle is inscribed in the circle x2 + y2 = a2 with the vertex at (a, 0). The equation of the side opposite to this vertex is

Q7

The lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 square units. An equation of this circle is (π = 22/7)

Q8

The equation f a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

Q9

A line is drawn through the point P(3, 11) to cut the circle x2 + y2 = 9 at A and B. Then PAPB is equal to

Q10

If the point (1, 4) lies inside the circle x2 + y2 – 6x – 10y + p = 0 and the circle does not touch or interest the coordinates axes, then