The endpoints of a diameter of a circle are (2, 4) and (-4, 7). What is the standard form of the equation of this circle? Enter

Question

The endpoints of a diameter of a circle are (2, 4) and (-4, 7).
What is the standard form of the equation of this circle?
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Sigridomena 4 years 2021-08-13T03:44:55+00:00 1 Answers 12 views 0

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    2021-08-13T03:46:54+00:00

    Answer:

    (x+1)²+(y-5.5)²=45/4.

    Step-by-step explanation:

    1)  the common form of the required equation is: (x-a)²+(y-b)²=r², where ‘a’ and ‘b’ are the coordinates of the centre of the given circle, r – radius of the given circle.

    2) the midpoint of the diameter is the centre of the given circle, its coordinates are:

    \frac{2-4}{2}=-1; \ and \ \frac{4+7}{2}=5.5.

    3) the length of the radius of the given circle is:

    r=\frac{1}{2}*\sqrt{(2+4)^2+(4-7)^2)}=\sqrt{\frac{45}{4}}.

    4) according to the common form and calculated the centre O(-1;5.5) and the radius it is possible to make up the required equation of the circle:

    (x+1)^2+(y-5.5)^2=\frac{45}{4}.

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