The equation of a circle C, with centre O, is:

Mathematics

1 answer:

Nataliya [291]3 years ago

8 0

Answer:

a) The center coordinates O is (0,0)

b) The radius C = 15

Step-by-step explanation:

The given equation of the circle is : $x^{2} + y^{2} = 225$

Now, general form of the equation of the circle is:

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

where (h,k) are the center co -ordinates and r is the radius of the circle.

Comparing the general equation with the given equation, we get

$(x-0)^{2} + (y - 0)^{2} = (15)^{2}$

So, here the center coordinates (h,k) = (0,0)

And the radius of the given circle is r = 15

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We have two points describing the diameter of a circumference, these are:

$\begin{gathered} A=(-12,-4) \\ B=(-4,-10) \end{gathered}$

Recall that the equation for the standard form of a circle is:

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

Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.

For this we use the following equation:

$M=(\frac{x_1+x_2_{}_{}}{2},\frac{y_1+y_2}{2})$

Now, we replace and solve:

$\begin{gathered} M=(\frac{-12+(-4)}{2},\frac{-4+(-10)}{2} \\ M=(\frac{-12-4}{2},\frac{-4-10}{2}) \\ M=(\frac{-16}{2},\frac{-14}{2}) \\ M=(-8,-7) \end{gathered}$

The center of the circle is (-8,-7), so:

$\begin{gathered} h=-8 \\ k=-7 \end{gathered}$

On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation: