The set of points on the axis of the parabola `y^2=4x+8` from which the three normals to the parabola are all real and different is `{(k ,0)"|"klt=-2}` (b) `{(k ,0)|k>>-2}` `{(0, k)"|"k >-2}` (d) none of these

Options

A. `{(x,0):xle-2)}`
B. `{(x,0):xgt-2)}`
C. `{(0, y):ygt-2)}`
D. none of these

Answer

D

Explanation

We have , `y^(2)=4(x+2)`
This represents a parabola with vertex (-2, 0) and axis x-axis We know that distinct normals can be drawn from a point on the axis of a parabola if its distance from the vertex is more than the semi-latusrectum.
So, three distinct normals can be drawn to the parabola `y^(2)=4(x+2)` if its distance from the vertex is more then 2 units. Let (h, 0) be such a point. Then,
`h+2gthgt0.`
Hence, te required set is `{(x, 0):gt0)}`.