# equation-geometrical

• Oct 31st 2007, 08:16 AM
lra11
equation-geometrical
1. Find the value for c for which y=x+c is a tangent to y=3-x-5x^2

don't understand what to do :(
• Oct 31st 2007, 08:32 AM
Krizalid
You gotta find first the intersection of the line and the curve, so

$x+c=3-x-5x^2\implies5x^2+2x+(c-3)=0.$

Now, so that the line be tangent to the curve, the discriminant of the previous equation must be zero, so $4-4\cdot5(c-3)=0\implies1-5(c-3)=0.$

Solvin' for $c$ yields the desired answer.
• Oct 31st 2007, 08:32 AM
red_dog
The system formed by the two equations must have an unique solution.
Plug y from the first equation in the second and you'll obtain a quadratic equation. Put the condition that $\triangle =0$, where $\triangle =b^2-4ac$ (a,b,c are the coefficients of the quadratic equation).