If `a!=0` and the line `2b x+3c y+4d=0` passes through the points of intersection of the parabolas `y^2=4a x` and `x^2=4a y ,` then `d^2+(2b+3c)^2=0` `d^2+(3b+2c)^2=0` `d^2+(2b-3c)^2=0` none of these

Options

A. `d^(2)+(2b-3c)^(2)=0`
B. `d^(2)+(3b+2c)^(2)=0`
C. `d^(2)+(3b-2c)^(2)=0`
D. `d^(2)+(3b+2c)^(2)=0`

Answer

D

Explanation

Parabolas `y^(2)=4ax" and "x^(2)=4ay` omtersect at points O(0, 0) and P(4a, 4a).
It is given that the line 2bx+3xy+4d=0 passes through O and P.
`:.` 4d=0 and 8ab + 12ac +4d = 0
`hArr" d=0 and 2b + 3c=0"hArrd^(2)+(2b+3c)^(2)=0`