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Find the center and radius of the circle whose equation is 5x^2+2x+5y^2-3y-19=0

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2 Answers

5 X2  + 2X + 5 Y2  - 3y  -19 = 0
 
5 ( X2 + 2/5 X ) + 5 ( Y2 - 3y ) = 19
 
5 ( X2  + 2/5 X + 1/25)  + 5 ( Y2 -3/5y +9/100  ) = 19 +1/5  + 45/100 
 
   5 ( X + 1/5 ) 2  + 5 ( Y - 3/10)2 = (1900 + 20 + 100)/100
 
      ( X + 1/ 5)  + ( Y - 3/10)2  = 2020/ 500 = 4.04 (**)
 
 
    Centre: ( -1/5, 3/10)  radius = 2 
  
   So, basically have to convert the expression to the form of ( **), by adding and subtracting quantities from both sides
  first you factor out 5 from 5X2, 5 Y2
 then make every parenthesis a perfect square, by adding quantities on both sides, and simplify it.
 
 
See my answer to your previous question. Here you first need to divide by 5. Then proceed like I did in the previous example.