Consider the parabola `y^(2)=8x,` if the normal at a point P on the parabola meets it again at a point Q, then the least distance of Q from the tangent at the vertex of the parabola is

Options

A. `16`
B. `8`
C. `0`
D. None of these

Answer

A

Explanation

`P-=(at_(1)^(2),2at_(1)),Q-=(at_(2)^(2),2at_(2))`, then
`t_(2)=-t_(1)-(2)/(t_(1))`
Here `4a =8" " therefore a=2`
Required distance,
`z=at_(2)^(2)=2(t_(1)^(2)+(4)/(t_(1)^(2))+4)=2[(t_(1)-(2)/(t_(1)))^(2)+8...(i)`
`implies zge2(8)]...(i)`
`therefore "least value of" z=16 ["from" (i)]`