# fixed point?

• Dec 30th 2005, 03:40 AM
ling_c_0202
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?
• Dec 30th 2005, 04:22 AM
CaptainBlack
Quote:

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

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

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

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

RonL
• Jan 1st 2006, 01:46 AM
ling_c_0202
thank you
:p thank you very much!