Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Using the focus and the directrix, the equation of the parabola is given by:
- [tex]x + 8 = \frac{3}{4}(y - 5)^2[/tex]
What is the equation of a parabola?
The equation of a parabola, with a directrix in x, is:
[tex]x - h = a(y - k)^2[/tex]
In which:
- The value of a is [tex]\frac{C}{4}[/tex].
- The vertex is (h,k).
- The focus is (h + C, k).
- The directrix is x = h - C.
In this problem:
- The directrix is x = -5, hence:
[tex]h - C = -5[/tex]
- The focus is (-11,5), hence:
[tex]h + C = -11[/tex]
[tex]k = 5[/tex]
Then, for the coefficients h and C:
[tex]h - C = -5[/tex]
[tex]h + C = -11[/tex]
Adding the equations:
[tex]2h = -16[/tex]
[tex]h = -\frac{16}{2} = -8[/tex]
[tex]C = -11 - h = -3[/tex]
[tex]a = \frac{C}{4} = \frac{3}{4}[/tex]
Hence, the equation of the parabola is:
[tex]x + 8 = \frac{3}{4}(y - 5)^2[/tex]
You can learn more about equation of a parabola at https://brainly.com/question/17987697
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
