﻿ The locus of the centre of the circle passing through the origin O and the points of intersection of any line through (a, b) and the coordinates axis is a : Kaysons Education

# The Locus Of The Centre Of The Circle Passing Through The Origin O and The Points Of Intersection Of Any Line Through (a, b) And The Coordinates Axis Is A

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## Question

### Solution

Correct option is

None of these

Equaition of the circle through (0, 0), (l, 0) and (0, m) is x2 + y2 – lx – my = 0, centre is (l/2, m/2).

#### SIMILAR QUESTIONS

Q1

Equation of a tangent to the circle with centre (2, –1) is 3x + y = 0. The squar  of the length of the tangent to the circle from the point (23, 17) is

Q2

The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid-point of the line segment joining the centres of C1 and C2 and C be a circle touching C1 and C2externally. If a common tangent to C1 and C passing through P is also a common tangent to 2 and C1, then the radius of the circle C is

Q3

An equation of the circle through (1, 1) and the points of intersection ofx2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0 is

Q4

The abscissae of two points A and B are the roots of the equation x2 + 2ax – b2 = 0, and their ordinates are the roots of the equation x2 + 2px –q2 = 0. The radius of the circle with AB as diameter is

Q5

The locus of the point of intersection of the tangent to the circle x = r cos θ, y = r sin θ at points whose parametric angles differ by

is

Q6

The locus of a point which moves such that the tangents from it to the two circles x+ y2 – 5x – 3 = 0 and 3x2 + 3y2 + 2x + 4y – 6 = 0 are equal is

Q7

If the two circles x2 + y2 + 2gx + 2fy = 0 and x2 + y2 + 2g1x + 2f1y = 0 touch each other, then

Q8

If two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 cut the coordinates axes in concyclic points, then

Q9

The locus of the point which moves in a plane so that the sum of the squares of its distances from the lines ax + by + c = 0 and

bx – ay + d = 0 is r2, is a circle of radius.

Q10

Four distinct point (1, 0), (0, 1), (0, 0) and (tt) are concyclic for