Question

the tangent to the curve y^2-xy+9=0 is vertical when...
i need some help with this :/

Answer 1

this should be in math instead of physics n u got more ppl helping u there too :)

u know the tangent is given by the differential of a function is given by dy/dx right?

Answer 2

implicit differentiation:
2yy' - y - xy' = 0
y'(2y - x) = y
y' = y/(2y-x)

what happens when 2y = x ??

to solve, first check for homogeneity
ky/(2ky - kx) = y/(2y-x) , thus box ticked

so sub y = vx, thus y' = v + v'x; and crank it out.