The condition that the parabolas `y^2=4c(x-d)` and `y^2=4ax` have a common normal other than X-axis `(agt0,cgt0)` is

Options

A. (1, 1, 1)
B. (1, 3, 2)
C. (1, 3, -2 )
D. (3, 2, 1)

Answer

B

Explanation

`y^2 = 8ax " and " y^2 = 4b ( x - c)`
tangent `y = mx + (2a)/(m)`
` y = m (x - c) + b/m therefore (2a)/(m) = - mc + b/m`
`mc = b/m - (2a)/(m)`
` mc = ( b- 2a)/(m)`
Since `m ne 0 therefore m^2 = (b - 2a)/(c ) `
` b gt 2a " and " c gt 0`
or
b < 2a < and c < 0
` therefore ` Possible choice of (a, b, c) is (1, 3, 2)