Question

What is the center and radius of the circle with the given equation?
x^2 + y^2 +10x - 6y = -9
Someone please help me or teach me or explain

Answer 1

do you know how to complete the square...?

Answer 2

if you group things

\[(x^2 + 10x ) + (y^2 -6y) = -9\]

each set of brackets on the left hand side need to contain perfect squares...

and the process of completing the square is essential to solving this problem.

Answer 3

No im not really good at this.

Answer 4

ok... so its easy....

the middle term is double the product of x and a number so find the number

looking at the x part

double the product is 10x

so halve it

5x so 5 and x are the factors...

so add 5^2 to get a perfect square....

this needs to be done to both sides of the equation..

so you get

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

see if you can work on the y-part

Answer 5

Oh thanks so is y=3 ?

Answer 6

and would the radius be 25?

Answer 7

well 2y*? = -6y

divide both sides by 2y

? = -3

so square it and add it to both sides of the equation.

Answer 8

Ohhhhhhh okay -6/2 = -3y

Answer 9

How can i find the radius?

Answer 10

ok... so what was the squared value you added to both sides of the equation... ?

Answer 11

ok... so the equation becomes

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

factor the 2 quadratic equations.... they are perfect squares... and simplify the right hand side

then the standard for of the circle is

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

the centre is (h, k) and the radius is r

hope this helps