Maximum number of common chords of a parabola and a circle can be equal to
(A) $ 2 $
(B) $ 4 $
(C) $ 6 $
(D) $ 8 $
VerifiedHint: To get the maximum number of common chords, the parabola and circle must intersect at maximum number of points.
Complete step-by-step answer:
Observe the diagram
From the diagram it is clear that the maximum number of points at which a parabola and a circle can intersect are 4.
Again, as shown in the diagram, we can draw 6 chords by joining the common points of parabola and circle. Namely, AB, AC, AD, CD, BC, BD
Therefore, maximum number of common chords of a parabola and a circle can be equal to 6
Therefore, from the above explanation, the correct option is (C) 6
So, the correct answer is “Option C”.
Note: This question can also be solved numerically. For that, we would write the general equation of the parabola and the general equation of the circle. Then we would solve them. But since both, the equation of parabola and the equation of circle are of degree two. The resultant equation would have been of degree 4. Which would be difficult to solve. Solving such questions using diagrams saves time and is comparatively easy if you know the diagram and its properties well.
