√[(x-4)^+y^2]=6-x

To simplify, y 2 = 20 (x+1) is the locus equation of point m.

2. The hyperbola x2/5-y2/3= 1 asymptote equation is y= plus or minus (b/a b/a) x = (√ 3/√ 5) x x.

That is, b/a=√3/√5.

b^2/a^2=3/5

c^2=a^2+b^2=64

The solution is a 2 = 40 and b 2 = 24.

So the hyperbolic equation is x 2/40-y 2/24 =1or x 2/24-y 2/40 =1.

(Because the focus can be on the X axis or the Y axis)