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What is the equation of the parabola with a focus at (0,0) and a directrix of y= -3?

Answer 1

The equation of the parabola is #y=1/6*x^2-1.5#

Vertex is at mid point between focus#(0,0)#and directrix #(y=-3)#So vertex is at #(0,-1.5)# The equation of parabola is#y=a(x-0)^2-1.5=ax^2-1.5# Distance(d) of vertex from directrix is 1.5 and we know #d=1/(4|a|) or a = 1/(4*1.5)=1/6#Hence the equation of the parabola is #y=1/6*x^2-1.5# graph{1/6*x^2-1.5 [-10, 10, -5, 5]}

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Answer 2

Savannah Anderson

The equation of the parabola with a focus at (0,0) and a directrix of y= -3 is ( y = \frac{1}{4}x^2 ).

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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.