If the gradient of one of the lines `x^2+h x y+2y^2=0` is twice that of the other, then `h=`

If the gradient of one of the lines x^(2)+hxy+2y^(2)=0 twice that of the other , then sum of possible values of h ____________.

The slope of one of the straight lines ax^(2)+2hxy+by^(2)=0 is twice that of the other, show that 8h^(2)=9ab .

If the slope of one of the lines represented by a x^2+2h x y+b y^2=0 is the square of the other, then (a+b)/h+(8h^2)/(a b)= (a) 4 (b) 6 (c) 8 (d) none of these

If the x intercept of the line y = mx + 2 is greater than 1/2 then the gradient of the line lies in the interval

If the pair of straight lines a x^2+2h x y+b y^2=0 is rotated about the origin through 90^0 , then find the equations in the new position.

Statement 1 : If -2h=a+b , then one line of the pair of lines a x^2+2h x y+b y^2=0 bisects the angle between the coordinate axes in the positive quadrant. Statement 2 : If a x+y(2h+a)=0 is a factor of a x^2+2h x y+b y^2=0, then b+2h+a=0 Both the statements are true but statement 2 is the correct explanation of statement 1. Both the statements are true but statement 2 is not the correct explanation of statement 1. Statement 1 is true and statement 2 is false. Statement 1 is false and statement 2 is true.

If the pair of lines a x^2+2h x y+b y^2+2gx+2fy+c=0 intersect on the y-axis, then prove that 2fgh=bg^2+c h^2

If one of the lines of the pair a x^2+2h x y+b y^2=0 bisects the angle between the positive direction of the axes. Then find the relation for a ,b ,h

If one root of the equation 2y^(2)-ay+64=0 is twice the other then find the values of a.