Question

A parabola has a focus of F(−11,5) and a directrix of x=−12. The point P(x,y) represents any point on the parabola, while D(−12,y) represents any point on the directrix. Miguel was asked to use the distance formula to write an equation to represent this parabola. Here is his work: FP=DP Step 1: (x−(−11))2+(y−5)2−−−−−−−−−−−−−−−−−−−√=(x−(−12))2+(y−y)2−−−−−−−−−−−−−−−−−−−√ Step 2: (x−(−11))2+(y−5)2=(x−(−12))2+(y−y)2 Step 3: x2+22x+121+y2−10y+25=x2+24x+144 Step 4: y2−10y+2=2x Step 5: 12y2−10y+1=x 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 3 is incorrect because he expanded the first binomial incorrectly.
Step 5 is incorrect because a previous step is incorrect.
only
Step 5 is incorrect because he divided incorrectly.
Step 1 is incorrect because he used the wrong signs for the coordinates of the focus.
Step 2 is incorrect because the square roots cancel the squares.
Step 3 is incorrect because a previous step is incorrect.
Step 4 is incorrect because a previous step is incorrect.

Answer 1

Step 5 is incorrect because a previous step is incorrect

Explanation:

Step 1 correct

Step 2 correct

Step 3 correct

Step 4 incorrect: It must be

y² - 10y + 25 = 2x + 23

Step 5 incorrect because step 4 incorrect

Step 5 must be : 1/2(y - 5)² - 23/2 = x