Prove that for all values of m, except zero the straight line
y = mx + touches the parabola y2 = 4ax.
If the tangent to the parabola y = x(2 - x) at the point (1, 1) intersects the parabola at P. Find the coordinate of P.
The given equation of parabola is,
y = x(x - 2) ...(i)
On differentiating, w.r.t. x, we get
Slope of tangent at (1, 1).
m = 2 - 2(1) = 0
Equation of tangent at (1, 1) is
(y - 1) = 0(x - 1)
On solving Eqs. (i) and (ii), we get
Thus, coordinates of point P are (1, 1)
If an unbiased coin is tossed n times. Find the probability that head appears an odd number of times.