- #1
TonyC
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Fins an equation for the parabola with focus at (-5,0) and vertex at (-5,-4).
I have come up with:
x^2 + 10x + 16y + 89 = 0
How far off am I?
I have come up with:
x^2 + 10x + 16y + 89 = 0
How far off am I?
TonyC said:Fins an equation for the parabola with focus at (-5,0) and vertex at (-5,-4).
I have come up with:
x^2 + 10x + 16y + 89 = 0
How far off am I?
The equation of a parabola with focus (h,k) and vertex (h,k-p), where p is the distance between the focus and vertex, is (x-h)^2=4p(y-k).
The direction of opening of a parabola is determined by the sign of the coefficient of x^2 in the equation. If it is positive, the parabola opens upwards, and if it is negative, the parabola opens downwards.
No, the focus and vertex of a parabola cannot be the same point. The vertex represents the lowest or highest point on the parabola, while the focus is a point inside the parabola. Therefore, they must be distinct points.
To graph a parabola with focus (h,k) and vertex (h,k-p), first plot the focus and vertex points on the coordinate plane. Then, use the distance p to plot two more points on either side of the vertex, making sure they are equidistant from the focus. Finally, draw a smooth curve connecting the four points to complete the parabola.
The axis of symmetry of a parabola is a vertical line that divides the parabola into two equal halves. For a parabola with focus (h,k) and vertex (h,k-p), the axis of symmetry is the line x=h. In this case, the axis of symmetry is the line x=-5.