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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
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