Answered

A parabola can be drawn given a focus of (-11, -5) and a directrix of x=−5. Write the equation of the parabola in any form.

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