Let two paraboles have a common axis where focus of each being exterior to the other and lt `l_(1),l_(2)` be their latus rectums then the locus of the mid points of the intercepts between the parabolas made on the lines parallel to the common axis is a

Options

A. Straight line if `l_(1)=l_(2)AAl_(1),l_(2)in R^(+)`
B. Parabola if `l_(1)nel_(2)AAl_(1),l_(2)inR^(+)`
C. Parabola`AAl_(1),l_(2) in R^(+)`
D. Hyperbola if `l_(1)=2l_(2)AAl_(1),l_(2)in R^(+)`

Answer

A, B

Explanation

`p_(1):y^(2)=l_(1)x`
`P_(2):y^(2)=-l_(2)(x-b)`
point on `P_(2)(y^(2)/(l_(1)),y)` and `P_(2) (b-y^(2)/(l_(2)),y)`
find locus of midpoint of above points