# Curves + Tangents

• Aug 20th 2009, 12:10 AM
xwrathbringerx
Curves + Tangents
Hi guys

I've been doing some revision for my yearlies and I'm stuck on these questions:

1) Find the values of m for which the curves y = mx and y = abs(sinx) have only one common point.

2) Show that, if the line y = mx + c is a tangent to the curve 4x^2 + 3y^2 = 12, then c^2 = 3m^2 + 4.

3) The curves with equations y = 4/x + 2 and y = ax^2 + bx + c have the following properties:
1. there is a common point where x = 2
2. there is a common tangent where x =2
3. both curves pass through the point (1,6)
Find the values of a, b and c.

The question nr 1 is very easy if you design the graph of the functions $\displaystyle y=mx$ and $\displaystyle y=|\sin x|$. The two curves have only one common point in $\displaystyle x=0$ if $\displaystyle |m|\ge 1$...
A little more interesting would be the research of the values of $\displaystyle m$ for which $\displaystyle y=mx$ and $\displaystyle y= \sin x$ have only one common point (Wink) ...
$\displaystyle \chi$ $\displaystyle \sigma$