The solution of `(dy)/(dx)=(a x+h)/(b y+k)` represent a parabola when (a) (a) ` a=0,b!=0` (b)` a!=0,b!=0` (c) ` b=0,a!=0` (d) ` a=0,b in R `

Let f(x)=(ax + b )/(cx+d) . Then the fof (x)=x , provided that : (a!=0, b!= 0, c!=0,d!=0)

The asymptotes of the hyperbola x y=h x+k y are (a) x-k=0 and y-h=0 (b) x+h=0 and y+k=0 (c) x-k=0 and y+h=0 (d) x+k=0 and y-h=0

The condition on a and b , such that the portion of the line a x+b y-1=0 intercepted between the lines a x+y=0 and x+b y=0 subtends a right angle at the origin, is (a) a=b (b) a+b=0 (c) a=2b (d) 2a=b

Let the parabolas y=x(c-x)a n dy=x^2+a x+b touch each other at the point (1,0). Then (a) a+b+c=0 (b) a+b=2 (c) b-c=1 (d) a+c=-2

If 1 is a twice repeated root of the equation a x^3+b x^2+b x+d=0,t h e n (a) a=b=d (b) a+b=0 (c) b+d=0 (d) a=d

The straight line a x+b y+c=0 , where a b c!=0, will pass through the first quadrant if (a) a c >0,b c >0 (b) ac >0 or b c 0 or a c >0 (d) a c<0 or b c<0

A circle with center (a , b) passes through the origin. The equation of the tangent to the circle at the origin is (a) a x-b y=0 (b) a x+b y=0 (c) b x-a y=0 (d) b x+a y=0

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

If the line a x+b y+c=0 is a normal to the curve x y=1, then a >0,b >0 a >0,b >0 (d) a<0,b<0 none of these

Two pairs of straight lines have the equations y^2+x y-12 x^2=0 and a x^2+2h x y+b y^2=0 . One line will be common among them if. (a) a+8h-16 b=0 (b) a-8h+16 b=0 (c) a-6h+9b=0 (d) a+6h+9b=0