the locus of the midpoint of a chord of the circle is x2+y2=4 which subtends a rightangle at the orgin is
please answer my question sir
The chord will be hypotenuse of the right angled triangle with remaining two sides being the radius of the circle, which is 2.
The length of hypotenuse = (22+22) = 22
The length of 1/2 hypotenuse = 2
The length of perpendicular bisector, (22-2) = 2
Let the coordinates of the midpoint of the chord be (x,y).
The distance from origin, (x2+y2) = length of perpendicular bisector = 2
Squaring both sides,
x2+y2 = 2,
Hence the locus is a circle with radius 2.