A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Derive the equation of the parabola with a focus at (4, −7) and a directrix of y = −15. Put the equation in standard form.
anonymous
 one year ago
Derive the equation of the parabola with a focus at (4, −7) and a directrix of y = −15. Put the equation in standard form.

This Question is Closed

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1ok... have you plotted the information on the number plane so you know the concavity of the parabola..?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So, you can still use the combined distance equation for this problem. But you just have to make your solution ax^2+bx+c=0.

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1so is the directrix above or below the focus...? and then is the parabola concave up or down..?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438892282167:dw so you plot looks like this

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438892378795:dw the distance is labelled 2a and is double the focal length.

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1the dotted line through x = 4 is the line of symmetry.... and the vertex is on this line midway between the focus and directrix

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1great so if the twice the focal length is 8 then the focal length is a = 4 so the vertex is 4 units below the focus on the line x = 4 so where do you think the vertex is..?

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1dw:1438892601545:dw

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1great... so the standard form I use now is \[(x  h)^2 = 4a(y  k)\] (h, k) is the vertex and a is the focal length so the equation is \[(x 4)^2 = 4 \times 4(y + 11)\] now you just need to simplify this equation

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1so if you want it in vertex form its \[\frac{1}{16}(x 4)^2 = y + 11\] then subtract 11 from both sides

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1well not quite \[\frac{1}{16}(x^2  8x + 16) 11 = y\]

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1which would become \[y = \frac{x^2}{16}  \frac{x}{2}  10 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh ok, thats the same as 1/16x^21/2x10 right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok thank you so much :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.