Thread: fixed point?

I don't know how to do

HKCEE 1993 Paper I 10(c),

even I read the solution already.



C is the curve y = 1/(k+1) ( 2(x)^2 + (k + 7)x + 4 )

Show that C always passes through two fixed points for all values of k not equal to -1. What are the coordinates of the two points?

Originally Posted by ling_c_0202

I don't know how to do

HKCEE 1993 Paper I 10(c),

even I read the solution already.



C is the curve y = 1/(k+1) ( 2(x)^2 + (k + 7)x + 4 )

Show that C always passes through two fixed points for all values of k not equal to -1. What are the coordinates of the two points?

Take two cases of the family of curves and generated
by letting and respectively.

Then find the x-coordinates of the points of intersection of
and (you should find these are and ).

Now substitute these values of back into the RHS of the equation of
and you will find that it is independent of .

So the points corresponding to the values of that you have found are
the same on all the curves (when ).

RonL

thank you very much!