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