SOLUTION: Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center p

Algebra ->  Graphs -> SOLUTION: Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center p      Log On


   

Question 202522: Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points.
a. (X+2)2 + (Y-4)2 = 36
I need help learning to solve for x and y (those are squared by the way) and how to find the slope so I can graph it.
Found 2 solutions by solver91311, Earlsdon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Any equation of the form is a circle centered at the point having radius


John

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, in this type of problem (identifying curves from their equations), it is helpful to recognise the standard form of the equation for a circle with its centre at (h, k) and having a radius of r:
%28x-h%29%5E2%2B%28y-k%29%5E2+=+r%5E2
Do you see the similarity between this and the given equation?
%28x%2B2%29%5E2%2B%28y-2%29%5E2+=+36: h = -2, k = 2, and r%5E2+=+36 so that r+=+6
Can you take it from here?
By the way, you do not have to solve for x or y to answer the question.
But you will have to solve for y to graph the equation.
Here's how you would do this:
%28x%2B2%29%5E2%2B%28y-2%29%5E2+=+36 Subtract %28x%2B2%29%5E2 from both sides of the equation.
%28y-2%29%5E2+=+-%28x%2B2%29%5E2%2B36 Now take the square root of both sides.
y-2+=+sqrt%28-%28x%2B2%29%5E2%2B36%29 Add 2 to both sides to isolate the y.
y+=+2%2B-sqrt%28-%28x%2B2%29%5E2%2B36%29 You can simplify the radicand (the quantity under the radical sign) a bit.
y+=+2%2B-sqrt%28-x%5E2-4x%2B32%29
Notice that you really have two answers here:
y+=+2%2Bsqrt%28-x%5E2-4x%2B32%29 and y+=+2-sqrt%28-x%5E2-4x%2B32%29 and, to graph this, you would have to graph both parts, one for the upper half of the circle and the other for the lower half.