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Give the equation of the circle centered at the origin and passing through the point (-4,0).D=D...

Question

Give the equation of the circle centered at the origin and passing through the point (-4,0).D=D

Give the equation of the circle centered at the origin and passing through the point (-4,0). D=D



Answers

Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.)
$$
(0,4)
$$

Okay, So this problem, because the centers at 00 we know that this equation for this circle is going to start with this X squared plus y square. However, in this case, they did not give it a straightforward radius that has told us that one of the points is gonna be 45 She's in the distance formula we confront. The radius is equal to the square root of four money zero square. We're just 16 post five minus zero squared, which is 20 time and so r equals the square root of 41. And therefore, R squared is just equal to 41. Thank you very much.

Center, but we're not given their radius. So we need to find a Raiders by. Look at here. The circle going through the arching which is there is zero so we can find Ah, radios here echo too distant region centre and the Irish in. So you were equal to the square Root off One stream on is zero square plus. Now I'm on a zero square. We get a co discoverer of the night plus 81 ico juice. Grassroot off. Ah, 90 on. Then we can write down the question Physical under form X minus Ministries square Plus Why? I'm honest. Nice square Coaches are square. Cut your nightie. We can rest on its express three square us. Well, I'm honest. Nice. Grab a coat your night day that this would be the answer here.

Problem tells us that the center of the circle is at the 0.35 and we have a point on the circle. That is the origin. So the radius or I guess we just need radius squared. It's gonna be the difference in our access squared, which is nine. And the difference in our wives squared. Just 25 nine plus 25 is just people to 34. Okay, so the equation this circle is gonna be x minus three square coastline minus five. Square is equal to 34 very much.

Hi. Welcome to name a raid. So this question is right. The equation off the circle that passes through the point negative five comma zero and has its center at the origin. So essentially, we're looking for the unique equation of a circle that both has the center at its origin, Um, and also passes through this plane's It's gonna be a unique equation, and we're gonna go ahead and find it. So the first thing you want to do when you're solving this type of problem if you want to go ahead and write out the general equation of a circle and that is X minus H squared plus y minus k squared equals R squared. So here h is tthe e x coordinate of the center of a circle. Kay is the y coordinate of the center of the circle and ours the radius of our circle. So the next step to do is to plug in what we know, what the center. So because these air to the two centre coordinates, we already know them from the problem itself. So we know that at the word at the origin X zero and at the center, which is the origin. Why is also zero? This is our new equation. And so we're gonna go ahead and simplify it down a little bit. So we have X squared plus y squared equals R squared. So the next step is to put in Thies this coordinate into our equation, and we're gonna look for the radius of the circle, and that will be the last part of our problem. So here we have X equals negative five and we have y equals zero. So we're gonna go ahead and plug that in. So we have negative five squared plus zero squared equals r squared. So then we can go ahead and multiply that. So we have 25 was r squared and we can see that Are is five right? So now we have the radius of a circle, and all we have to do is write out the equation of this new circle we found. So we'll start with E general equation for this for a circle. So you have X minus h squared. Plus why minus k squared equals R squared. So the center of the circle is still at the origin, so we go ahead and put a zero in for H and K, And we also know what the radius of our circle is. And we know that's five. So we know that this is gonna be five squared, so we're gonna head and simplify that down a bit x squared. Plus why squared equals 25. And this is the equation of a circle that passes through the point X equals negative five weikel zero and has a center at the origin.


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