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What is the vertex form of the equation of the parabola with a focus at (17,14) and a directrix of #y=6 #?

Answer 1

The equation of parabola in vertex form is #y=1/16(x-17)^2+10#

The vertex is at midpoint between focus#(17,14)# and directrix #y=6:.#The vertex is at#(17,(6+14)/2) or (17,10):.#The equation of parabola in vertex form is #y=a(x-17)^2+10#Distance of directrix from vertex is #d=(10-6)=4 :. a=1/(4d)=1/16:.#The equation of parabola in vertex form is #y=1/16(x-17)^2+10# graph{y=1/16(x-17)^2+10 [-80, 80, -40, 40]} [Ans]

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Answer 2

Kennedy Adams

The vertex form of the equation of the parabola with a focus at (17,14) and a directrix of y=6 is:

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

where the vertex (h, k) is the midpoint between the focus and the directrix, and ( p ) is the distance between the vertex and the focus (or between the vertex and the directrix).

So, the equation becomes:

[ (x - 17)^2 = 8(y - 10) ]

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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.