Find the center and radius

Question

X^2+4x+y^2+6y=8

With steps

 

Answer 1

Hi Kennedy,

 

You need to complete the square in order to get the equation in the standard form for the equation of a circle:

 

(x-h)² + (y-k)² = r²

 

So,

 

(x² + 4x + ___ ) + ( y² + 6y + ____) = 8

 

What values go in the blanks to make the trinomials perfect square trinomials. And whatever values you supply must also be added to the right side of the equal sign (addition property of equality).

 

Looks like 4 to complete the square for the first blank and 9 for the 2nd blank.

 

Which means we have:

 

(x+2)² + (y+3)² = 8+4+9

 

So center is at (-2,-3) and radius is √21

 

 

Answer 2

Hi Kennedy,

 

Adding both the sides 4 & 9 to make perfect square,

 

x² +4x +4 +y² +6y +9 =8+4+9

(x+2)² +(y+3)² =21

 

Equation of a circle with Center (h,k) & radius r would be,

 

(x-h)² +(y-k)² =r² .

 

comparing, we get center of a circle (-2,-3) & radius =√21