9876543210
everything's fuzzy..
T(ct,c/t) is a point on the rectangular hyperbola xy=c^2. The point M is the foot of the perpendicular drawn from the origin O to the tangent to the hyperbola at T.
i) Show that the tangent to the hyperbola at T has equation x+t^2 y-2ct=0
ii) Find the coordinates of M.
iii) Find the equation of the locus of M as T moves on the rectangular hyperbola.
i've solved the first two parts but i cant work the third out.
the answer for iii) (x^2 +y^2)^2=4c^2 xy
help please
thx
i) Show that the tangent to the hyperbola at T has equation x+t^2 y-2ct=0
ii) Find the coordinates of M.
iii) Find the equation of the locus of M as T moves on the rectangular hyperbola.
i've solved the first two parts but i cant work the third out.
the answer for iii) (x^2 +y^2)^2=4c^2 xy
help please
thx
