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horrorfan [7]
2 years ago
10

1. A circle with center (-5, 2) is tangent to the y-axis. What is the radius of the circle? What is the equation of the circle?

Mathematics
1 answer:
Bess [88]2 years ago
4 0

Answer:

Step-by-step explanation:

1)  The center lies on the vertical line x = -5 and the the circle is tangent to (touches in one place only) the y-axis.  Thus, the radius is 5.

2)  Starting with (x - h)^2 + (y - k)^2 = r^2 and comparing this to the given

                     (x - 4)^2 + (y + 3)^2 = 6^2

we see that h = 4, k = -3 and r = 6.  The center is at (4, -3) and the radius is 6.

3)  Notice that A and B have the same x-coordinate, x = 15.  The center of the circle is thus (15, -2), where that -2 is the halfway point between the two given points in the vertical direction.   Arbitrarily choose A(15, 4) as one point on the circle.  Then the equation of this circle is

(x - 4)^2 + (y + 3)^2 = r^2 = 6^2, where the 6 is one half of the vertical distance between A(15, 4) and B(15, -8) (which is 12).

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  2. Parenthesis
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<u>Algebra II</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle 3^{6x + 18} < 27^{3x}<em />

<em />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Rewrite:                                                                                                             \displaystyle 3^{6x + 18} < 3^{3(3x)}
  2. Set:                                                                                                                     \displaystyle 6x + 18 < 3(3x)
  3. Factor:                                                                                                               \displaystyle 3(2x + 6) < 3(3x)
  4. [Division Property of Equality] Divide 3 on both sides:                                  \displaystyle 2x + 6 < 3x
  5. [Subtraction Property of Equality] Subtract 3x on both sides:                       \displaystyle -x + 6 < 0
  6. [Subtraction Property of Equality] Subtract 6 on both sides:                        \displaystyle -x < -6
  7. [Division Property of Equality] Divide -1 on both sides:                                 \displaystyle x > 6
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