Find the values of k, if the equation `8x^(2)-16xy + ky^(2) - 22x + 34y = 12` respresents an ellipse.

For what value of k, do the equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines ?

Show that the equation 3x^(2)+4y^(2)-12x-8y+4=0 represents an ellipse. Find the focus also

Find the values of k for which the equation x^2+5k x+16=0 has no real roots.

The equation 16x^(2)+y^(2) +8xy-74x-78y+212 =0 represents

Find the value of k for which equation 4x^(2)+8x-k=0 has real and equal roots.

Find the value of k, if x=2, y=1 is a solution of the equations 2x+3y=k .

Find the value of k , if x=2, y=1 is a solution of the equations 2x+3y=k .

Find the value of k for which the system of equations 2x + ky = 1 and 3x - 5y = 7 has a unique solution.

Find the value of k , if x=2 and y=1 is a solution of the equation 2x+3y=k .

For what value of lambda does the equation 12x^2-10xy+2y^2+11x-5y+lambda=0 represent a pair of straight lines ? Find their equations and the angle between them.