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Degger [83]
3 years ago
12

Find the equation for the circle with a diameter whose endpoints are (-5, -3) and (3,2).

Mathematics
1 answer:
densk [106]3 years ago
3 0

Answer:

  (x +1)^2 +(y +0.5)^2 = 22.25

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is ...

  (h, k) = ((-5, -3) +(3, 2))/2 = (-5+3, -3+2)/2 = (-1, -1/2)

The circle formula is then ...

  (x -h)^2 +(y -k)^2 = r^2

  (x -(-1))^2 +(y -(-1/2))^2 = r^2

We can find r^2 by substituting one of the points for (x, y).

  (3 +1)^2 +(2 +1/2)^2 = r^2 = 16 +6.25 = 22.25

Then the circle equation is ...

  (x +1)^2 +(y +0.5)^2 = 22.25

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Step-by-step explanation:

I will solve your system by substitution.

(You can also solve this system by elimination.)

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8x

8

=

10

8

(Divide both sides by 8)

x=

5

4

Step: Substitute

5

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forxiny=−3x+2:

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y=−3(

5

4

)+2

y=

−7

4

(Simplify both sides of the equation)

Answer:

x=

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and y=

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