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` `a<<0,b>>0` (d) `a<0,b<0` none of these

Find the equation of the normal to the curve x^2/a^2-y^2/b^2=1 at (x_0,y_0)

The equation to the normal to the curve y=sinx at (0,\ 0) is (a) x=0 (b) y=0 (c) x+y=0 (d) x-y=0

The lines parallel to the normal to the curve x y=1 is/are 3x+4y+5=0 (b) 3x-4y+5=0 4x+3y+5=0 (d) 3y-4x+5=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=b (b) a+b=0 a=2b (d) 2a=b

The lines parallel to the normal to the curve x y=1 is/are (a) 3x+4y+5=0 (b) 3x-4y+5=0 (c) 4x+3y+5=0 (d) 3y-4x+5=0

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are in (a). A.P. (b). G.P. (c). H.P. (d). none of these

If the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurrent, then a , b , c are in a. H.P. b. G.P. c. A.P. d. none of these

The equation of the plane through the intersection of the plane a x+b y+c z+d=0\ a n d\ l x+m y+n+p=0 and parallel to the line y=0,\ z=0. (A) (b l-a m)y+(c l-a n)z+d l-a p=0 (B) (a m-b l)x+(m c-b n)z+m d-b p=0 (c) (n a-c l)d+(b n-c m)y+n d-c p=0 (D) None of these

If the lines a x+2y+1=0,b x+3y+1=0a n dc x+4y+1=0 are concurrent, then a ,b ,c are a. A.P. b. G.P. c. H.P. d. none of these

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