y=kx+1 is tangent to ..

therefore, they have a unique common point, say (a,b), that satisfies both equation.. so and

if we equate the , we have

this is a quadratic equation hence, we can solve for the value of a:

we want a unique solution for a, so we set the discriminant be equal to 0..

.. solve for k.. Ü

if a is the lenth of the longer side, then a-7 is the length of the shorter side,

since "hypotenuse" came, it can be assumed that this is a right triangle, hence .. do the algebra..