The line `2x+y+lamda=0` is a normal to the parabola `y^(2)=-8x,` is `lamda`=

Options

A. ` - 24 `
B. `8 `
C. `-16 `
D. `24 `

Answer

A

Explanation

Given , parabola , `y^ 2 = 8x `
` rArr 2y ( dy )/ ( dx ) = 8 `
` rArr (dy ) / ( dx ) = ( 4 )/( y ) `
Slope of normal of parabola = ` - ( y )/ ( 4 ) ` … (i)
Given ` 2x + y + lamda = 0 ` is a equation of normal of the parabola ` y ^ 2 = 8 x `.
` therefore ` Slope of normal ` = - 2 " " `... (ii)
From Eqs. (i) and (ii) , we get
` - ( y ) /(4 ) = - 2 rArr y = 8 `
` therefore (8) ^ 2 = 8 x rArr x = 8 `
Now, putting the values of x and y in the equation of normal
` 2 ( 8 ) + 8 + lamda =0 `
` rArr lamda = -24 `