Question

A parabola and a circle are graphed into the standard (x,y) coordinate plane. The circle has a radius of 4 and is centered at (1,1). The parabola, which has a vertical axis of symmetry, has its vertex at (1,5) and a point at (2,4). How many points of intersection exist between the parabola and the circle?

Answer 1

Correct answer: Two point of intersection and one touch point.

Explanation:

Cartesian form of parabola is: y= a(x-1)² + 5 and point named A(2,4)

when we replace the coordinates of the point A in the formula we get

a = - 1 and parabola is y= - (x-1)² + 5 which means that it faces the opening downwards. The parabola touches the circle in vertex.

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