Thursday, October 15, 2009

Parabola and Circle

A circle intersects the parabola y=x^2 at the points (1,1), (2,4), and (3,9). Find the fourth point of intersection.
Posted by at
Labels:

1 comment:

  1. DavidOctober 24, 2009 at 6:23 AM

    The answer is (-6, 36).

    The equation of the circle has the form
    x^2 + y^2 + ax + by + c = 0.

    After substituting y = x^2, we have
    x^2 + x^4 + ax + bx^2 + c = 0.

    This is a fourth-degree equation, and the sum of the roots is zero, because the coefficient of x^3 is zero.

    It is given that 1, 2, and 3 are roots. So the fourth root must be -6, and so the fourth point of intersection is (-6, 36).

    ReplyDelete

Subscribe to: Post Comments (Atom)