Multiple choice

If $OA$ and $OB$ are two perpendicular chords of the circle $r=a\cos { \theta } +b\sin { \theta }$ passing through origin, then the locus of the mid point of $AB$ is:

  1. ${x}^{2}+{y}^{2}=\dfrac{ax}2+\dfrac {by}2$
  2. $x=a/2$
  3. ${x}^{2}-{y}^{2}={a}^{2}+{b}^{2}$
  4. $y=b/2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation r = a*cos(theta) + b*sin(theta) represents a circle passing through the origin. Converting to Cartesian: x^2 + y^2 = ax + by. The midpoint of perpendicular chords OA and OB through the origin satisfies the locus x^2 + y^2 = (ax/2) + (by/2).

Keep practicing — related questions