help me anwer this math ploblem?

Question

What is the equation of the circle with center (3, 5) that contains the point (3, -1)?

Answer 1

The general equation of a circle is (x - a)² + (y - b)² = r² with (a,b) as the center and r as the radius.

In this equation, a = 3, b = 5.
The radius is the distance between the given point and the center. This one is easy to figure out without much math, as the x coordinate is 3. So if you draw it out, you can see that the point given is directly above the center. The distance is just 5 - (-1) = 6.

That said, plug the numbers back in the equation. (x - 3)² + (y - 5)² = 6²

So the equation of this circle is:
(x - 3)² + (y - 5)² = 36.

Answer 2

Two ways of solving this. The easier one is plotting the points Center(3,-1) and another point say A(3,5). For a circle to contain the point A, means that A is on one side of the arc formed with a radius distance of 6 (5 units above the x line and one unit below the x-line). Or, r^2 = 36.

Now, the general formula of a circle is (x-h)^2 + (y-k)^ = r^2.
Substituting values, this becomes (x-3)^2 + (y-5)^2 = 36. Further, you can FOIL, and rearrange to get x^2 -6x +y^2 -10y = 0. But then, this last one is not easily recognizable as an equation of a circle. The previous equation is preferred.

Or. you can find the distance from the point A to the center using the distance formula. This will give you the value for the radius.
You should get the same answer.

Answer 3

davit is right

the equation for a circle would be (x-h)^2 + (y-k)^2 = r^2 where h and k are the respective x and y coordinates of the circle. All you now need to know is the radius which you would get with the distance formula and that will be 6. Then square the radius as depicted in the equation. You will get (x-3)^2 + (y-5)^2 = 36

Answer 4

The general equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2.

The radius for this circle is 6 units; that's the distance between points (3,5) - the center and (3,-1) which is on the circumference.

Thus, the equation of the circle becomes:
(x-3)^2 + (y-5)^2 = 36

Simplifying, you get:
x^2 - 6x + 9 + y^2 - 10y + 25 = 36
or
x^2 - 6x + y^2 - 10y - 2 = 0

Answer 5

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Answer 6

I believe it's:

(x-3)^2 + (y-5)^2 = 6

Answer 7

(X-3)^2+(Y-5)^2=36

Answer 8

(x-5)^2+(y-3)^2=(-1-5)2+(3-3)^2
(x-5)^2+(y-3)^2=36