Question

Which of the following equations is of the parabola whose vertex is at (4, 3), axis of symmetry parallel to the y-axis and focus at (4, -3)?
A.) y+3=1/24 (x+4)^2
B.)y-3=-1/24 (x-4)^2
C.)x-4=-1/24 (y-3)^2

Answer 1

Answer:

B.

Step-by-step explanation:

First thing to determine is how this parabola opens.  Up or down? Or left or right?  

*We see that the axis of symmetry is a line parallel to the y-axis; therefore, the axis of symmetry is an x =    line, making this an up or down parabola.  Now we need to determine how everything else all fits in.

The standard form of this type of parabola is

$4p(y-k)=-(x-h)^2$

where p is the distance between the vertex and the focus.  If the vertex has a y coordinate of 3, and the focus has a y coordinate of -3, the vertical distance between those 2 numbers is 6.  Therefore, p = 6.  Filling in then:

$4(6)(y-3)=-(x-4)^2$

and $24(y-3)=-(x-4)^2$

Dividing both sides by 24 gives you what you are looking for:

$y-3=-\frac{1}{24}(x-4)^2$