Question

what is y form of x^(2)+y^(2)-3x+5y-11 = 0

Answer 1

Given equation x ^2 + y ^2 -3x + 5y - 11 = 0

To change the equation into a perfect square  add (half the x coefficient)²

And add (half the y coefficient)²  to each side of the equation.

 Here x  coefficient = -3. so, (half the x coefficient)² = (-3/2)²= 9/4

 Here y  coefficient = 5. so, (half the y coefficient)² = (5/2)²= 25/4

x ^2 + y ^2 - 3x + 5y - 11 + 9/4 + 25/4 -11 = 9/4 + 25/4

x ^2 - 3x + 9/4 + y ^2 + 5y + 25/4 - 11 = 9/4 + 25/4

(x - 3/2)^2 + (y + 5/2)^2 - 11 = 9/4 + 25/4

(x - 3/2)^2 + (y + 5/2)^2 = 9/4 + 25/4 + 11

(x - 3/2)^2 + (y + 5/2)^2 = (9 + 25 + 44)/4

(x - 3/2)^2 + (y + 5/2)^2 = 78/4

(x - 3/2)^2 + (y - (-5/2))^2 = 78/4

Compare it to standard form of circle equation (x - h )^2 + (y - k )^2 = r ^2.

(y - (-5/2))^2 = 78/4 - (x -3/2)^2

Apply squre root on each side.

y - (5/2) = ± √[78/4 - (x - 3/2)^2]

y  form of given equation is

y  = (5/2) ± √[78/4 - (x - 3/2)^2].