Question

Which equation helps determine the focal length, p, of a parabola?

A) 1 - a + b² = c²
B) 2 - x - h² = 4p(y - k)
C) 3 - y = mx + b
D) 4 - There is no equation.

Answer 1

The focal length of a parabola, represented by p, can be determined by the equation 4p(y - k) = (x - h)², which relates to the standard form of a parabolic equation, typically written as y = ax² + bx + c.

Step-by-step explanation:

The equation that helps determine the focal length, p, of a parabola is not directly listed among the options A to D. However, we know that the standard form of a parabolic equation is y = ax² + bx + c, where the coefficient a relates to the direction and width of the parabola. The focus of a parabola lies at the point (h, k + p), where (h, k) is the vertex of the parabola and p is the focal length. The correct equation is of the form 4p(y - k) = (x - h)², which is a rearranged version of the standard definition y = (1/(4p))(x - h)² + k when the parabola opens upwards. If the parabola opens to the right, the standard definition would be x = (1/(4p))(y - k)² + h.