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swat32
3 years ago
13

Given the vertex (2,9) and the foci (5,9), what is the equation of the directrix

Mathematics
1 answer:
Gennadij [26K]3 years ago
6 0

Answer:

x = -1

Step-by-step explanation:

The vertex is halfway between the focus and the directrix.

So here the directrix is  a vertical line  to the left of the vertex and passing through the point (2-3, 9) = (-1, 9)

It is x = -1.

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Use the discriminant to describe the roots of each equation. Then select the best description.
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The <em>quadratic</em> equation 3 · x² + 7 · x - 2 = 0 has a <em>positive</em> discriminant. Thus, the expression has two <em>distinct real</em> roots (<em>real</em> and <em>irrational</em> roots).

<h3>How to determine the characteristics of the roots of a quadratic equation by discriminant</h3>

Herein we have a <em>quadratic</em> equation of the form a · x² + b · x + c = 0, whose discriminant is:

d = b² - 4 · a · c     (1)

There are three possibilities:

  1. d < 0 - <em>conjugated complex</em> roots.
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If we know that a = 3, b = 7 and c = - 2, then the discriminant is:

d = 7² - 4 · (3) · (- 2)

d = 49 + 24

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The <em>quadratic</em> equation 3 · x² + 7 · x - 2 = 0 has a <em>positive</em> discriminant. Thus, the expression has two <em>distinct real</em> roots (<em>real</em> and <em>irrational</em> roots).

To learn more on quadratic equations: brainly.com/question/2263981

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