Geometry

A parabola has a focus of F(2,8.5) and a directrix of y=9.5. The point P(x,y) represents any point on the parabola, while D(x,9.5) represents any point on the directrix.

Maria was asked to use the distance formula to write an equation to represent this parabola.

Here is her work:

Step 1: FP=DP
Step 2: (x−2)2+(y−8.5)2−−−−−−−−−−−−−−−−√=(x−x)2+(y−9.5)2−−−−−−−−−−−−−−−−−√
Step 3: x2−4x+4+y2−17y+72.25=y2−19y+90.25
Step 4: x2−4x−14=−4y
Step 5: −14x2+x+72=y

Identify each incorrect step.

Select all answer choices that both state an incorrect step and explain why it is incorrect.

If there is only one incorrect step, select "only" and the answer choice that states and explains the incorrect step.

Step 5 is incorrect because she divided incorrectly.
Step 4 is incorrect because she added the y-terms incorrectly.
Step 3 is incorrect because a previous step is incorrect.
only
Step 5 is incorrect because a previous step is incorrect.
Step 4 is incorrect because a previous step is incorrect.
Step 3 is incorrect because she expanded the first binomial incorrectly.
Step 2 is incorrect because she used the wrong signs for the coordinates of the focus.
I don't understand this at all... please help!

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asked by lilbaby
  1. First, you need to learn how to type math.
    x^2 is x squared
    1/4 is a fraction; 14 is not

    step 1 is ok, since that is the definition of a parabola.
    step 2 is ok -- just use the distance formula
    step 3 is ok -- both sides squared
    step 4 is bad: -19+17 = -2, not -4
    step 5 is ok if you use correct text characters

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    posted by Steve
  2. Ty...

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    posted by lilbaby
  3. I actually got that incorrect.. but it was probably my fault... Thanks anyways

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    posted by lilbaby

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