## anonymous one year ago Derive the equation of the parabola with a focus at (−7, 5) and a directrix of y = −11. a) f(x) = −one eighth (x − 2)2 + 6 b)f(x) = one eighth (x − 2)2 + 6 c)f(x) = −one eighth (x + 2)2 + 8 d)f(x) = one eighth (x + 2)2 + 8

• This Question is Open
1. anonymous

2. anonymous

sec just making sure my numbers work

3. anonymous

thank you ive narrowed it down to either a or c but i dont know what to do for there

4. amistre64

one method is to define all points (x,y) that are equidistance from a focus (a,b) and a directrix (in this case y=k) - which is just the point (x,k) (x-a)^2 + (y-b)^2 = (x-x)^2 + (y-k)^2

5. amistre64

(x-a)^2 + y^2 -2by +b^2 = y^2 -2ky +k^2 (x-a)^2 -2by +b^2 = -2ky +k^2 (x-a)^2 +(b^2-k^2) = 2by -2ky (x-a)^2 +(b^2-k^2) = 2(b-k)y (x-a)^2/(2(b-k)) +(b^2-k^2)/(2(b-k)) = y (x-a)^2/(2(b-k)) +(b+k)/2 = y

6. amistre64

none of your options fit ...

7. anonymous

if you use the formula $y=a(x-h)^2+k$ where P = -7 Q = 5 and R = -11 and where a = $\frac{ 1 }{ 2Q-2R }$ H = P and $K = \frac{ Q + R }{ 2 }$ you can just plug in the values and solve

8. anonymous

I got that problem too.

9. amistre64

we know the options are bad or something off, since the parabola opens up its vertex x is the same value as the focus x ... (x+7)^2 is the main part

10. amistre64

its y value is the average of the focus y and the directrix (5-11)/2 = -3

11. amistre64

y = a(x+7)^2 - 3

12. anonymous

a = 1/32

13. amistre64

yep

14. amistre64

can you screen shot it?

15. anonymous

ya that's why I didn't reply faster... I was wondering if my math was bad or something haha

16. amistre64

some people tend to post the answers for one with the question of another

17. anonymous

oh my i am so sorry i realized the problem

18. anonymous

two of the questions were switched because those look like they would work for Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8

19. amistre64

never be afraid of your own errors ... they might prove to be correct int he end :)

20. anonymous

Using either of the 2 methods posted above with the new data should give you the answer :)

21. anonymous

thank yall sorry

22. anonymous

Np.

23. amistre64

good luck :)

24. anonymous

so its a

25. anonymous

thank you all so much that was very helpful