Principal Axes and Conic Section of Quadratic Equation 9x2

Principal Axes and Conic Section of Quadratic Equation 9x^2 + 6 xy + y^2 = 10

Solution

9x² + 6xy + y² = 10

( 3x )² + 2( 3x )( y ) + ( y )² = 10

( 3x + y )² = 10

( 3x + y ) = 10 or ( 3x + y ) = - 10

3x + y - 10 = 0 or 3x + y + 10 = 0

Therefore , the above conic equation denotes pair of straight lines .