algebra help?

Question

x^2 + y^2 - 6x + 10y - 2 = 0

Find the center and the radius of the circle with equation....


Im confused, any help would be appreciated!

Answer 1

(x ² - 6x + 9) + (y ² + 10y + 25) = 2 + 9 + 25
(x - 3) ² + (y + 5) ² = 6 ²
Centre (3 , - 5)
radius = 6

Answer 2

to start up, you must understand that the general equation for a circle is:

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

where (h,k) is the center [ h being referenced with x-axis and k with the y-axis]

and r is the radius

so all we need to do is to convert the given equation into a similar format as that of a circle. and to do that, follow these steps:

1] separate variables ( terms with x, y, x^2, y^2) from constants. this is done by writing all variables on the left side of the equation and constants on the right side. this step would result to:

x^2 +y^2 -6x +10y = 2

*** also take note that when taking a term from one side to the other side, change its sign with the opposite sign ( positive (+) to negative (-) or vice versa). In this case, notice the -2 changed to +2... this is called the law on transposition...

2]next group all similar terms on the left side of the equation. that is group all terms with 'x'. do the same thing with terms with 'y'.

(x^2 - 6x + ___ ) + ( y^2 + 10y + ___ ) = 2

***notice that i put a blank in each group. this is because on the next step, we will be completing the square and we need to put a constant on those blanks.

3] complete the square. In this step, we need to find out the constant to be put on the blanks in order to obtain a perfect square. To do this, just divide the number on the 1st degree term by 2 ( i'm referring to terms with the 'x' and 'y' --- in this equation that is -6x and 10y) and square the quotient..

so for the x terms
(-6 / 2 ) ^2 = 9

and for the y terms
(10/ 2) ^2 = 25

so to complete the equation, write the computed values on the blank:

(x^2 - 6x + 9) + (y^2 +10y + 25) = 2 + 9 + 25

*** note that whatever you added on the left side of the equation should also be added on the right side... that's why we have "= 2 + 9 + 25"

4] factor out the equation and arrive with this one:

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

or a more appropriate format based on equation of circle:

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

5] to get the center, consider the opposite sign:

so center is ( 3, -5) and NOT (-3, 5)

and radius is 6

Answer 3

x^2 - 6x + y^2 + 10y - 2 = 0
(x^2 - 6x + 3^2 ) + ( y^2 + 10 y + 5^2 ) -2 - 3^2 - 5^2 = 0
(x + 3)^2 + (y +5 )^2 = 2 + 9 + 25 = 36
(x + 3)^2 + (y +5 )^2 = 36 = 6^2
center = (-3, -5)
radius = 6

Answer 4

That's so........ Confusing!!! Sorry, I can't help you...