The point of intersection of the tangents at the ends of the latus rectum of the parabola `y^2=4x` is_____________

Answer

(-1,0)

Explanation

The coordinates of extremities of the latusrectum of `y^(2) = 4x` are (1,2) and (1,-2)
Equation of tangents at these points are
`y. 2 = (4(x + 1))/(2) implies 2y = 2 (x + 1)`
and `y (-2) = (4(x + 1))/(2)`
`implies -2y = 2 (x + 1)`
`:. -2 (x + 1) = 2 (x + 1)`
`implies 0 = 4 (x + 1)`
`implies - 1 = x implies y = 0`
Therefore, the required point is (-1,0)