SOLUTION: Hello, i have been given this maths question, please could you help me solve it. I have tried putting it into a quadratic equation then i realised that it cannot be factorised. The
Question 578107: Hello, i have been given this maths question, please could you help me solve it. I have tried putting it into a quadratic equation then i realised that it cannot be factorised. The question is:
prove that the line y+x=-2 is a tangent to the curve y^2 = 8x
Thank you Answer by Edwin McCravy(20054) (Show Source):
A line which intersects a parabola exactly once and which is not
parallel to the axis of symmetry, is tangent to the parabola.
y + x = -2 is a tangent to the curve y² = 8x
The axis of symmetry of that parabola is the
x-axis, and the line y + x = -2 is not parallel
to the x-axis, so if it intersects the parabola
exactly once, then it is tangent to the parabola.
We solve the equation of the line for y
y + x = -2 - x
y = -2 - x
And we substitute (-2 - x) for y in
y² = 8x
(-2 - x)² = 8x
4 + 4x + x² = 8x
x² - 4x + 4 = 0
(x - 2)(x - 2) = 0
x - 2 = 0, x - 2 = 0
x = 2 x = 2
Th fact that -2 is a double root for x shows that
there is just one point of intersection and so the
line is tangent to the parabola at the point were
x = 2, which has y-coordinate y = -2 - (2) = -4
or the point (2,-4) is the point of tangency.
Edwin
