SOLUTION: a) If x^2 + y^2 + 4x -2y +1=, show that (x+2)^2 + (y-1)^2 =4 b) x^2 + y^2 - 6x - 8y =0 can be written in the form (x - a)^2 + (y+b)^2= c, find the values of a,b and c

Algebra ->  Equations -> SOLUTION: a) If x^2 + y^2 + 4x -2y +1=, show that (x+2)^2 + (y-1)^2 =4 b) x^2 + y^2 - 6x - 8y =0 can be written in the form (x - a)^2 + (y+b)^2= c, find the values of a,b and c      Log On


   

Question 1115398: a) If x^2 + y^2 + 4x -2y +1=, show that (x+2)^2 + (y-1)^2 =4
b) x^2 + y^2 - 6x - 8y =0 can be written in the form (x - a)^2 + (y+b)^2= c, find the values of a,b and c
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a)
x%5E2+%2B+y%5E2+%2B+4x+-2y+%2B1=0
%28x%5E2+%2B+4x%29+%2B+%28y%5E2+-2y%29+=-1 ....complete squares
%28x%5E2+%2B+4x%2Bb%5E2%29-b%5E2+%2B+%28y%5E2+-2y%2Bb%5E2%29+-b%5E2=-1
use the rule: %28x%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2
since you have first term x%5E2 and middle term 4x, means that coefficient a=1 and 2ab=4=>2b=4=>b=2
and
since you have first term y%5E2 and middle term -2y, means that coefficient a=1 and 2ab=-2=>2b=-2=>b=-1
then, you have
%28x%5E2+%2B+4x%2B2%5E2%29-2%5E2+%2B+%28y%5E2+-2y-1%5E2%29+-%28-1%29%5E2=-1
%28x%2B2%29%5E2-4+%2B+%28y+-1%29%5E2+-1=-1
%28x%2B2%29%5E2+%2B+%28y+-1%29%5E2+=4%2B1-1
+%28x%2B2%29%5E2+%2B+%28y-1%29%5E2+=4


b)
x%5E2+%2B+y%5E2+-+6x+-+8y+=0 written in the form %28x+-+a%29%5E2+%2B+%28y-b%29%29%5E2=+c ( %28y%2Bb%29%5E2 is wrong, should be %28y-b%29%5E2)
%28x%5E2++-+6x%29+%2B+%28y%5E2-+8y%29+=0
%28x%5E2++-+6x%2Bb%5E2%29-+b%5E2%2B+%28y%5E2-+8y%2Bb%5E2%29+-b%5E2=0
%28x%5E2++-+6x%2B3%5E2%29-+3%5E2%2B+%28y%5E2-+8y%2B4%5E2%29+-4%5E2=0
%28x++-+3%29%5E2-+9%2B+%28y-+4%29%5E2%29+-16=0
%28x++-+3%29%5E2%2B+%28y-+4%29%5E2%29+=9%2B16
%28x++-+3%29%5E2%2B+%28y-+4%29%5E2%29+=25

so, a=-3,b=-4 and +c=25