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tankabanditka [31]
2 years ago
7

write the standard form of the equation of the circle for which the endpoints of a diameter are (0,0) and (4,-6)

Mathematics
1 answer:
Elenna [48]2 years ago
5 0

Given:

The endpoints of a diameter are (0,0) and (4,-6).

To find:

The equation of the circle.

Solution:

The endpoints of a diameter are (0,0) and (4,-6). So, the length of the diameter is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

d=\sqrt{(-6-0)^2+(4-0)^2}

d=\sqrt{36+16}

d=\sqrt{52}

d=2\sqrt{13}

Now, radius is half of the diameter.

r=\dfrac{2\sqrt{13}}{2}

r=\sqrt{13}

Center of the circle is the midpoint of the endpoints of a diameter.

Center=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

Center=\left(\dfrac{0+4}{2},\dfrac{0+(-6)}{2}\right)

Center=\left(\dfrac{4}{2},\dfrac{-6}{2}\right)

Center=\left(2,-3\right)

Standard form of a circle is

(x-h)^2+(y-k)^2=r^2

where, (h,k) is center and r is radius.

The center of the circle is (2,-3) and radius is \sqrt{13}. So,

(x-2)^2+(y-(-3))^2=(\sqrt{13})^2

(x-2)^2+(y+3)^2=13

Therefore, the standard form of the circle is (x-2)^2+(y+3)^2=13.

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Answer:

3) 27 cubed

4) 72 cubed

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8) 27 cubed. 3 is the length, 3 is the width, and 3 is the height.

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Step-by-step explanation

Here's what to show if your teacher requires for you to show your work.

3) 3 x 3 x 3 = 27

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These are the ones I'd suggest putting the up and down form on.

10) and 5) Also put 5 x 5 = 25.          4) and 9) Also put 6 x 3 = 18.

     <em>2                                                        3</em>

     25                                                      18

  <u>x  5 </u>                                                     <u>x 4  </u>

   125                                                      72

Hoped this answered everything! Feel free to ask me if there's something I missed! :)

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