Two tangent are drawn from the point `(-2,-1)` to parabola `y^2=4xdot` if `alpha` is the angle between these tangents, then find the value of `tanalphadot`

Answer

3

Explanation

(3) Any tangent to the parabola `y^(2)=4x,(a=1)`, is
`y=mx+(1)/(m)`
It passes through (-2,-1). Therefore,
`-1=-2m+(1)/(m)`
`or2m^(2)-m-1=0`
`or(2m+1)(m-1)=0`
`orm=-(1)/(2)andm=1`
Then the angle between the lines is
`tantheta=|(m_(1)+m_(2))/(1-m_(1)m_(2))|=3`