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3. Fid the equation for the circle show &t the right:3M...

Question

3. Fid the equation for the circle show &t the right:3M

3. Fid the equation for the circle show &t the right: 3M



Answers

Write an equation for the circle with center $\mathrm{A}(-3,-2)$ and radius 3.

We need to find the equation off the circle whose centre lies at point minus one minus three and radius is given to be three. Now we know that the commission of the circle is scared off X minus H plus scare off my mind. Escape is equal to be our skin. We're HK represent the center of the circle and artista radius off the circle. Never putting the value off the coordinates off the center of the circle. And we're putting the value of radius. This become skittle X plus three X plus one plus scare off. Why plus three is equal. Toby three. Skill. Now we can rewrite it as scare off X plus one plus scare off by plus three is equal. Toby nine. So this is the required decoration off the circle. Who's the center? Lies at point minus one minus three and whose ideas is equal to be three. So this is our answer

So the verdict. Texas 00 And then the radius, they say, is square root of three. The formula says ex Monas, the X coordinate will X minus zero is just expo while I'm on a zero is just why? And if we're going to square this squaring the square root basically cancels out and we're left with just three, so this will be the equation of our circle.

Question Uses center of 00 for a circle. The centers that 00 and it gives you a radio and it says the first of all right, Nick Lesion and then half circle. It's pretty easy to graft the circle, even if you don't have the right occasion because the centers at 00 and the radius is three, something's gonna go. 1230 here and three up And then three back years 0123 in the negative direction. And then 123 down as well. You get basically the circle looked like this. It kind of goes around. I'm not good at drawing circles, but you get the idea. So there's graph. The equation of the circle is always This is the General for the equation. That circle where Agent K that I'm writing and here are the center of a circle and our is the radius. So you get X squared because the h zero you get, why squared? Because the que is euro all right, because the center is at 00 So that's H, and that's case of this becomes zero that becomes a girl, which means they attempt to go away, right? You get to act weird and white in an aren't. We're just 39. That's the equation of that circle.

Okay, so let's find the equation of a circle centered at the origin that passes through the 0.0 negative three right here. And so since we were given a point and this is an ex point in a why point, we can use the standard form of the equation to find, um, the radius of the circle. And then we can write our final answer. And since we so since we move zero units to the left, right or up and down because it's centered at the origin, the H and the K values we can just moment. So since our X value given is zero weaken right zero squared plus the Y value given his minus three were also square. That's a minus three squared, and that is eagle to R squared. So zero squared is just zero minus three squared is gonna be a positive nine is equal to R squared. So we know that three is equal to are. So you know, the radius of our circle here it's gonna be three. So now we can write our final answer. So we're gonna write and x squared, and then it's just X squared because it's not shifted left or right? It all. We're gonna add to it a y squared because it's not shifted up or down all we know that the radius is three. But we need the radius squared value to put over here on the right side of the equation. So we're gonna set that equal tonight, and that is the equation of a circle centered at the origin that passes through the point zero minus three.


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