Respuesta :

slysoph
(x + 8)^2 + (y - 15)^2 = 17^2

Equation of a circle
Midpoint at (a,b)

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

You know what the circle’s center is so you can substitute those values in

(x + 8)^2 + (y - 15)^2 = r^2

But you don’t know what the radius is. To find the radius, we know that the circle passes through the origin (0,0) so you just use the distance formula to figure out the radius length.

Distance formula:

Square root of (x1 - x2)^2 + (y1 - y2)^2

So...

Square root of (-8 - 0)^2 + (15 - 0)^2
Square root of 64 + 225
Square root of 289
r=17

So you substitute 17 into the equation of a circle formula and the result is:

(x + 8)^2 + (y - 15)^2 = 17^2

~~hope this helps~~

The equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].

What is the general equation for the circle?

The general equation of the circle is [tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex].

Where, (h, k) is the center and r is the radius of the circle.

Let the equation of the circle be

[tex](x-h)^{2} +(y-k)^{2} =r^{2}..(i)[/tex]

According to the given question.

The center of the circle is (-8, 15).

⇒ (h, k) = (-8, 15)

And, the circle is passing through origin i.e. (0, 0).

Since, the center of the circle is (-8, 15).

So, the equation (i) can be written as

[tex](x-(-8))^{2} +(y - 15)^{2} = r^{2}[/tex]

Also, the circle is passing through (0, 0).

Therefore,

[tex](0+8)^{2} +(0-15)^{2} = r^{2}[/tex]

[tex]\implies 64+ 225 = r^{2} \\\implies 289 = r^{2} \\\implies r=\sqrt{289} \\\implies r = 17[/tex]

So, the radius of the circle is 17 unit and its center is (-8, 15).

Therefore, the equation of the circle is

[tex](x+8)^{2} +(y-15)^{2} = 289[/tex]

Hence, the equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].

Find out more information about equation of circle here:

https://brainly.com/question/10618691

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