How many common chords can a circleparabola have?

Dear shubham

there can be maximum of 4 points of intersection

so max no.of chords will be 6

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Prudhvi Teja

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This is because there is a maximum four points of intersection between a parabola and circle. You can show this algebraically:Say the parabola`s equation is x2=4ay and the circle`s equation is x2+y2+2fx+2gy+h=0 then by substituting y=x2/4ay into the circle`s equation, we get:x4/16a2+x2+2fx+2gy+h=0 which is a degree 4 polynomial hence has at max 4 distinct real roots hence 4 different points of intersection (since the parabola equation is many to one).With 4 points of intersection you can then form a common chord by choosing any two of the four points by using permutation and joining them; hence you can have at max 4C2=6 common chords.