Find the radius of the circe with the equation x^2+y^2-6x-12y+36=0?

Answer 1

The general form of the equation of a circle is:

(x-k)^2 + (y-h)^2 = r^2

where the ordered pair (k,h) represents the center of the circle and r = radius.

To get the x and y squared terms, you need to form a perfect square.

For the x terms, you have [x^2-6x]. You can deduce that you should get the perfect square term (x-3)^2 because when you FOIL this out, you get a -6x term. (x-3)^2 = x^2-6x+9, thus you need a '9' term to complete the above perfect square.

Using the same logic for the y term, you have [y^2-12y], thus the perfect square you can deduce is (y-6)^2. FOILing this out, you get y^2-12y+36, thus you need a '36' term to complete the perfect square.

To get these constant terms, we just need to rewrite the constant value in a different way.

Thus, you get

(x^2-6x+9) + (y^2-12y+36) - 9 = 0

If you combine the constant terms in this equation, you still get 36 because 9+36-9 = 36. Now you can solve for the general form of a circle:

(x-3)^2 + (y-6)^2 = 9

Using the general form of the circle equation, you can conclude that r^2 = 9. Therefore, radius = 3

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Hope this helps

Answer 2

Get it in a form of a² + b² = c² and the answer will be c...

Start by grouping the x-terms and y-terms on one side:
x² - 6x + y² - 12y = -36

Now complete the squares. You do this by taking half the coefficient on the x term (or y term) and squaring it.

So:
For x² - 6x, you take half -6 (-3) and square it (-3)² = 9
So add a 9 to both sides:

(x² - 6x + 9) + y² - 12y = -36 + 9 = - 25

Now you can write that as a perfect square:
(x - 3)² + y² - 12y = -25

Continue completing the square for the y-terms:
y² - 12y, take half -12 (-6) and square it (-6)² = 36

So add this again to both sides:
(x - 3)² + (y² - 12y + 36) = -25 + 36 = 9

Once again you can now express y as a square:
(x - 3)² + (y - 6)² = 9

And turn the right side into a square:
(x - 3)² + (y - 6)² = 3²

This is now in the form a² + b² = c²
Your radius (c) is 3.

The answer is the radius is 3 units.

Answer 3

g=3,f=6 c=36
radius=rt(g^2+f^2-c)
=rt(9+36-36)
=rt9
=3 units

Answer 4

(x-3)^2+(y-6)^2=9
Therefore, the radius is 3.

Answer 5

sorry but i don't math alot

Answer 6

No. You find it.