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 gradient of one of the lines x^2+h x y+2y^2=0 is twice that of the other, then 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 two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisect the angle between the other two, then the value of c is (a) 0 (b) -1 (c) 1 (d) -6

The two lines represented by 3a x^2+5x y+(a^2-2)y^2=0 are perpendicular to each other for (a)two values of a (b) a (c)for one value of a (d) for no values of a

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 a tangent of slope 2 of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is normal to the circle x^2+y^2+4x+1=0 , then the maximum value of a b is 4 (b) 2 (c) 1 (d) none of these

The straight lines represented by the equation 135 x^2-136 x y+33 y^2=0 are equally inclined to the line (a) x-2y=7 (b) x+2y=7 (c) x-2y=4 (d) 3x+2y=4

The straight lines represented by (y-m x)^2=a^2(1+m^2) and (y-n x)^2=a^2(1+n^2) from a (a) rectangle (b) rhombus (c) trapezium (d) none of these

Through a point A on the x-axis, a straight line is drawn parallel to the y-axis so as to meet the pair of straight lines a x^2+2h x y+b y^2=0 at B and Cdot If A B=B C , then (a) h^2=4a b (b) 8h^2=9a b (c) 9h^2=8a b (d) 4h^2=a b