How many common chords can a circle parabola have?

Prudhvi teja
83 Points
13 years ago

Dear shubham

there can be maximum of 4 points of intersection

so max no.of chords will be 6

Please feel free to post as many doubts on our discussion forum as you can.we will get you the answer and detailed  solution very  quickly.

All the best.

Regards,
Prudhvi Teja

Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian

Prashant
24 Points
5 years ago
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.