Here is a simple mechanics question. A 1 kg block is at rest on a rough plane inclined at 30 degree angle to the horizontal. Find the magnitude and direction of the reaction force of the plane on the block.
Sorry that I misled you. I wonder why my mistakes were not pointed out.
d^2=2a/(a+b) is ok. Points 0f contact of the 2 curves are at x=y=+/-sqrt(a/(a+b)), and gradient =-1.
Hence b=0 and d=sqrt2.
y(ax+by)=c, x^2+y^2=d^2
using given info,
x(ax+bx)=a, x^2+x^2=d^2
.: d^2=2a/(a+b) and the hyperbola must be tangential to the circle which requires a=b
.: d=1