1. ## fixed point?

I don't know how to do

HKCEE 1993 Paper I 10(c),

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?

2. Originally Posted by ling_c_0202
I don't know how to do

HKCEE 1993 Paper I 10(c),

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 $\displaystyle C_1$ and $\displaystyle C_2$ generated
by letting $\displaystyle k=1$ and $\displaystyle k=2$ respectively.

Then find the x-coordinates of the points of intersection of
$\displaystyle C_1$ and $\displaystyle C_2$ (you should find these are $\displaystyle -1$ and $\displaystyle -2$).

Now substitute these values of $\displaystyle x$ back into the RHS of the equation of
$\displaystyle C$ and you will find that it is independent of $\displaystyle k$.

So the points corresponding to the values of $\displaystyle x$ that you have found are
the same on all the curves (when $\displaystyle k \neq -1$).

RonL

3. ## thank you

thank you very much!