Question

find the centre and radius of 2 X square + 2 Y squared minus x is equal to zero

Answer 1

2xsquare +2y square -x=0

center (-g, -f) =(1/2,0)
radius root of g square +f square -c=rootof( 1/2)whole square +0 square -0= 1/2

Answer 2

Answer:

(1/4, 0) and r = 1/4

Step-by-step explanation:

Consider the given equation 2 x^2 + 2 y^2 – x = 0

                                     2(x^2 + y^2 – x/2) = 0

             So we get x^2 + y^2 – x/2 = 0  

          Now x/2 can be written as 2(1/4)

 So  x^2 + y^2 – 2(1/4)x = 0

  Now add and subtract ¼ to both sides. This is done because we can bring it to the form of (a – b) ^2 = a^2 + b^2 – 2ab

       [ x^2 – 2(1/4) x + (1/4) ^2] – (1/4) ^2 + y^2 = 0

         (x – ¼) ^2 – (1/4) ^2 + y^2 = 0

        (x – ¼) ^2 + y^2 = (1/4) ^2

 We can write the above equation as  

        (x – ¼) ^2 + (y – 0) ^2 = (1/4) ^2

The above equation is of the form (x – a) ^2 + (y – b) ^2 = r ^2

   So a = ¼, b = 0 and r = ¼  

Hence centre is (1/4, 0) and radius r = 1/4