Find the equation of the evolute of the parabola y? = 12x.

1. For the parabola equation: (y-2) = -3(x+4)^2 + 7, in which direction does the parabola open?

Solve for the directrix of the parabola y2 + 8x = 32

Solve the parabola and show the solution

An historic, parabolic arch which provides a walkway under a building can be modeled by the equation y = 36 -0.04x², with all values given in ft. What is the approximate width of the arch at its widest point, in ft, if y = 0 at ground level? width of arch at widest point = feet

Write the equation of the hyperbola of foci F1(2, −1), F2(2, 4) and focal radius difference equal to 3.

The equation for a parabola has the form y = ☛² + bx+c, where a, b, and care constants and a 0. Find an equation for the parabola that passes through the points (-1,4), (3,-8), and (4,-1). Answer: y

By completing the square, find the standard form of the equation of the parabola: y = x^2 + 6x + 7 B) Sketch the graph of the parabola:

Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse axis 6 and the curve passes through the point (7, -4).

A parabolic stream of water is spraying out of a hole in the floor two feet behind Veronica. The water is passing over her at a height of six feet. It then lands on the floor 18 feet in front of her. Write an equation for the stream of water.