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`

If the two circles 2x^2+2y^2-3x+6y+k=0 and x^2+y^2-4x+10 y+16=0 cut orthogonally, then find the value of k .

Find the angle at which the circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect.

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

If the two circles (x+1)^2+(y-3)=r^2 and x^2+y^2-8x+2y+8=0 intersect in two distinct point,then (A) r > 2 (B) 2 < r < 8 (C) r < 2 (D) r=2

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=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

If the circles x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0 and 2x^2+2y^2+2a x+2b y+c=0 intersect othrogonally, then prove that a a^(prime) + b b prime=c+c^(prime)/2dot

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

If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersects at points P and Q , then find the values of a for which the line 5x+b y-a=0 passes through Pa n dQdot

If the circle x^2+y^2=1 is completely contained in the circle x^2+y^2+4x+3y+k=0 , then find the values of kdot