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Rufina [12.5K]
3 years ago
8

What is the equation of the circle with Center (-6, 7) that passes through the point (4, -2) ​

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

we know the center of the circle, and we also know a point on the circle, well, the distance from the center to a point is just the radius.

\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[4-(-6)]^2+[-2-7]^2}\implies r=\sqrt{(4+6)^2+(-2-7)^2} \\\\\\ r=\sqrt{10^2+(-9)^2}\implies r=\sqrt{100+81}\implies r=\sqrt{181} \\\\[-0.35em] ~\dotfill

\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{7}{ k})\qquad \qquad radius=\stackrel{\sqrt{181}}{ r}\\[2em] [x-(-6)]^2+[y-7]^2=(\sqrt{181})^2\implies (x+6)^2+(y-7)^2=181

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The inequalities are matched with their correct graph respectively as follows:

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<h3>What is an inequality?</h3>

An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:

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In Geometry, if the leading coefficient of a quadratic equation is greater than (>) zero, the parabolic curve would open upward while the parabolic curve would open downward when the leading coefficient of a quadratic equation is less than (<) zero.

Read more on graph of inequalities here: brainly.com/question/24372553

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Complete Question:

Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)

1. A = {(x, y): y > x^2}

2. B = {(x, y): y ≥ x^2+ 3}

3. C = {(x, y): y ≤ 3x^2 + 2}

4. D = {(x, y): y ≥ 2x^2- 5x + 1}

6. x^2- 3x ≥ 0

7. x^2- 3x + 2 ≤ 0

8. {(x, y): y ≤ 1 - x^2}

9. {(x, y): y ≥ -1}

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