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3 years ago

Suppose a circle with center (14,9) passes through point (16, 12). Which equation represents the circle?

Mathematics

1 answer:

kifflom [539]3 years ago

8 0

Answer:

( x - 14)^2 + ( y - 9)^2 = 13

Step-by-step explanation:

The equation of the circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( 14 , 9) - center-( a, b)

a = 14

b = 9

( 16 , 12) - point - ( x, y)

x = 16

y = 12

Step 1: substitute the center into the equation

( x - 14)^2 + ( y - 9)^2 = r^2

Step 2: substitute the point into the equation

( x - 14)^2 +( y - 9)^2 = r^2

( 16 - 14)^2 + ( 12 - 9)^2 = r^2

2^2 + 3^2 = r^2

4 + 9 = r^2

13 = r^2

Step 3: subs the radius into the equation

( x - 14)^2 + ( y - 9)^2 = r^2

( x - 14)^2 + (y - 9)^2 = 13

Therefore, the equation of the circle is

( x - 14)^2 + ( y - 9)^2 = 13

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Step-by-step explanation: Let's start this problem by setting up a chart so we can organize our information that we're given in this problem.

Down the left side, we'll have our different types of coins. In this case dimes and quarters. Across the top we'll have our formula which is shown below.

Number of coins · value of each coin = total value

Now let's fill out our chart.

For number of dimes and quarters, we know that mark has a total of 17 dimes and quarters but we don't know how many of each he has. In fact, that's what the problem is asking.

So if we represent our number of dimes as x, we can call our number of quarters 17 - x.

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Our total value based on our formula is going to come from the first column times the second column. So the total value of our dimes is x times 10 or 10x and the total value of our quarters is 17 - x times 25 or 25 (17 - x).

Our goal in this problem will be to find x because x represents our number of dimes and the problem asks how many dimes does he have. If we know the number of dimes, we can easily find the number of dimes and we'll have our answer. However, we need an equation in order to find x.

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Going back up into our chart, remember that x represents our number of dimes so Mark has 12 dimes. To get his number of quarters, we take 17 - x which is 17 - 12 or 5 quarters and that's our answer.

I have also attached the chart that I have made below.

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