Find value of m for y = mx tangent to parabola y2 = 4(x - 1)

[simonjordan2008]

Consider the parabola y2 = 4(x − 1).

1. Find the values of m for which the line y = mx is tangent to the parabola.

2. For these values of m, state the coordinates at which the tangent meets the parabola.

3. Consider the line y = m(x − 2) and suppose this meets the parabola. Find the quadratic equation satisfied by the x-coordinate(s) of intersection. Hence by considering the number of roots to this equation, investigate whether the line y = m(x − 2) can ever be tangent to the parabola.

 

[arthur ohlsten]

Plot the curves
1) y^2=4[x-1]
some points are
x=1 y=0
x=2 y=+/-2
x=5 y=+/-4

y=mx a straight line
slope m
y intercept x=0 y=0

1)
y=x and y=-x are the two lines tangent to y^2=4[x-1]

2)
they are tangent at :
x=2 y=2 and x=2 y=-2

3)
y=m[x-2]
a straight line crossing the x axis at x=2
this line crosses the curve ffor all values of m for -oo<m<oo
It can never be tangent to the curve

Arthur