Q:

Find the coordinates of the focus and equation of the directrix for the parabola given byy2 = βˆ’4x.The general formula for this parabola is y2 = 4px.Therefore, the value of p is _____The coordinates of the focus are ______The equation of the directrix is ______

Accepted Solution

A:
Answer:The answers to your three problem question are shown1) the value of p is p = -12) The coordinates of the focus are Focus = Β (-1,0)3) The equation of the directrix is Directrix x = 1Step-by-step explanation:The general equation for this parabola isy^2 = 4pxProblem 1Find the value of p.We are told that the equation of the problem isy^2 = -4xAnd the general formula isy^2 = 4pxFrom there, we can deduce thatp = -1, becausey^2 = 4(-1)x = -4xThis means that p = -1Problem 2Find the focus To find the focus we can see the equations attached below for the focus, vertex and directrix.In these case, the equations still apply, even though the variable is inverted, we just need to adjust ity^2 = -4x =>x = (-1/4)*y^2x = a*y^2 + b*y +cFocus((4ac -b^2 Β + 1)/4a, -b/2a)But, b = 0 and c = 0=>(1/4a,0) = (1/4(-1/4),0) = (-1,0)Focus = Β (-1,0)Problem 3Find the directrix The equation isx = c - (b^2 + 1).4aBut, b = 0 and c = 0x = -4*ax = -4* (-1/4) = 1x = 1Directrix x = 1