Question

The coordinates of two point P and Q are (2, 3) and (3, 2) respectively. Circles are described on OP and OQ as diameters; O being the origin, then length of the common chord is

Solution

Correct option is

Equation of the circle are x2 + y2 – 2x – 3y = 0 and x2 + y2 – 3x – 2y = 0. Equation of the common chord is y = x, for the points of intersection 2x2 – 5x = 0 ⇒ x = 0, 5/2, length of the chord 

                                           

SIMILAR QUESTIONS

Q1

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  

Q2

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 

Q3

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 

Q4

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

Q5

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

Q6

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.  

 

Q7

The locus of the centre of the circle passing through the origin O and the points of intersection of any line through (ab) and the coordinates axis is a

Q8

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

Q9

If two circles which pass through the points (0, a) and (0, –a) cut each other orthogonally and touch the straight line 

y = mx + c, then

Q10

The circle x2 + y2 – 6x – 4y + 9 = 0 bisects the circumference of the circle x2 + y2 – (λ + 4)x – (λ + 2)y + (5λ + 3) = 0 if λ is equal to