write in standars notation xy28x4y190Solutionx2 y2 8x 4y

write in standars notation x^+y^2+8x+4y+19=0

Solution

x² + y² + 8x + 4y + 19 = 0

==> x² + 8x + y² + 4y + 19 = 0

==> x² + 2(4)x + 4² - 4² + y² + 2(2)y + 2² - 2² + 19 = 0

==> (x + 4)² + (y + 2)² - 16 - 4 + 19 = 0          since a² + 2ab + b² = (a + b)²

==> (x + 4)² + (y + 2)² -1 = 0

==> (x + 4)² + (y + 2)² = 1

Hence x² + y² + 8x + 4y + 19 = 0 in standard notation is (x + 4)² + (y + 2)² = 1