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What is the equation of the parabola with a focus at (15,19) and a directrix of y= 20?

Answer 1

The directrix is above the focus, so this is a downward opening parabola.

The vertex will lie exactly halfway between the directrix and the focus:

#"vertex"=(15,19.5)#

The distance #p# between the vertex and the focus is #p=1/2#, so the absolute value of the coefficient #abs(a) = 1/(4p)= 1/2# Now, since we know the parabola opens downward, the sign on the coefficient must be negative.

Here is the final equation:

#y=-1/2(x-15)^2+19.5#

hope that helped

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Answer 2

Eva Abramson

The equation of the parabola is (x - h)^2 = 4p(y - k), where (h, k) is the coordinates of the vertex and p is the distance from the vertex to the focus (or from the vertex to the directrix). So, the equation of the parabola with a focus at (15,19) and a directrix of y = 20 is (y - 19)^2 = 4(1)(x - 15).

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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.