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What is the standard form equation of the parabola with a vertex at (0,0) and directrix at x= -2?

Answer 1

Eva Abramson

#x = 1/8y^2#

Please observe that the directrix is a vertical line, therefore, the vertex form is of the equation is:

#x = a(y-k)^2+h" [1]"#

where #(h,k)# is the vertex and the equation of the directrix is #x = k - 1/(4a)" [2]"#.

Substitute the vertex, #(0,0)#, into equation [1]:

#x = a(y-0)^2 + 0#

Simplify:

#x = ay^2" [3]"#

Solve equation [2] for "a" given that #k = 0# and #x = -2#:

#-2 = 0 - 1/(4a)#

#4a = 1/2#

#a = 1/8#

Substitute for "a" into equation [3]:

#x = 1/8y^2 larr# answer

Here is a graph of the parabola with the vertex and the directrix:

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Answer 2

Avery Alexander

The standard form equation of the parabola with a vertex at (0,0) and directrix at x = -2 is ( y^2 = 4ax ), where a is the distance from the vertex to the focus and from the vertex to the directrix. Therefore, ( a = 2 ). So, the equation becomes ( y^2 = 8x ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.