I'm new to this website and how it works, but I would appreciate it if somebody helped me!

Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.

Question

I'm new to this website and how it works, but I would appreciate it if somebody helped me! 


Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.

phantomcrow · Answer

What did you notice when you graphed these two points on a plane?

anonymous · Answer

@Phantomcrow It opens to the right?

phantomcrow · Answer

Yes! And you know what the standard equation of a parabola that opens to the right is?

anonymous · Answer

@Phantomcrow Can you help me out with that one

anonymous · Answer

It is 3, you're welcome.

phantomcrow · Answer

Sure.|dw:1444091089825:dw|

phantomcrow · Answer

Since the vertex is at the origin, there is no need to add any constants for shifts. The graph is simply $$y^2=x$$

anonymous · Answer

@Phantomcrow 
By the way the Answer choices are


y= 1/28x^2

x= 1/28y^2

-28y= x^2

y^2=14x

What confuses me is how these tie to the standard formula

phantomcrow · Answer

D. Despite it having an 'x' term, its vertex is still at the origin.

phantomcrow · Answer

Standard form is one of the ways to write the graph of a parabola. It is commonly seen as:$$ax^2+bx+c$$

anonymous · Answer

@Phantomcrow Wow thanks, would it be cool if you helped me with one more?

phantomcrow · Answer

Sure

anonymous · Answer

@Phantomcrow Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8, i'm guessing this is similar or even exact to the last one, so it opens to the left

phantomcrow · Answer

Actually, it does not open to the left this time. You are given y values for focus and directrix, not x values.

anonymous · Answer

@Phantomcrow So y values open to the right and x values open to the left?

phantomcrow · Answer

Y values lie across a vertical line, you your parabola will be opening upwards. You can easier see this if you look at the (0.8) and y= -8 on a graph. See that the they are equidistant from a point.

anonymous · Answer

@PhantomCrow you graph (0,8) correct?

phantomcrow · Answer

Yes. Graph the point (0,8) and y= -8 and you should be able to visually see the the point that is equidistant from them. There is a formula for finding distance but I believe simply looking at the graph for this problem will provide you with the answer.

anonymous · Answer

@PhantomCrow The choices are 

y= 1/32x^2

y^2= 8x

y^2=32x

y=1/8x^2

Would it be B?

phantomcrow · Answer

Oh, I see.