The two curves `x=y^2,x y=a^3` cut orthogonally at a point. Then `a^2` is equal to `1/3` (b) 3 (c) 2 (d) `1/2`

The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0 cuts orthogonally

If the curves a y+x^2=7a n dx^3=y cut orthogonally at (1,1) , then find the value adot

The curve ay^2=x^2(3a-x) cuts the y - axis at .........

If the circles x^2+y^2+2x+2ky+6=0 and x^2+y^2+2ky+k=0 intersect orthogonally then k equals (A) 2 or -3/2 (B) -2 or -3/2 (C) 2 or 3/2 (D) -2 or 3/2

The locus of the midpoints of the chords of contact of x^2+y^2=2 from the points on the line 3x+4y=10 is a circle with center Pdot If O is the origin, then O P is equal to 2 (b) 3 (c) 1/2 (d) 1/3

The circle x^2 + y^2 - 3x - 4y + 2 = 0 cuts the x axis at the points

The line tangent to the curves y^3-x^2y+5y-2x=0 and x^2-x^3y^2+5x+2y=0 at the origin intersect at an angle theta equal to pi/6 (b) pi/4 (c) pi/3 (d) pi/2

The number of tangents to the curve x^(3/2)+y^(3/2)=2a^(3/2),a >0, which are equally inclined to the axes, is 2 (b) 1 (c) 0 (d) 4

If the graph of the function f(x)=(a^x-1)/(x^n(a^x+1)) is symmetrical about the y-a xi s ,then n equals 2 (b) 2/3 (c) 1/4 (d) 1/3

The curves 2x^(2) + 3y^(2) = 1 and cx^(2) + 4y^(2) = 1 cut each other orthogonally then the value of c is: