Find the equations of the chords of the parabola `y^2= 4ax` which pass through the point (- 6a, 0) and which subtends an angle of `45^0` at the vertex. (a) `y=+-(2)/(7)(x+6a)` (b) `y=+-(3)/(8)(x+6a)` (c) `y=+-(7)/(2)(x+6a)`
(d) `y=+-(5)/(6)(x+6a)`

Options

A. `y=+-(2)/(7)(x+6a)`
B. `y=+-(3)/(8)(x+6a)`
C. `y=+-(7)/(2)(x+6a)`
D. `y=+-(5)/(6)(x+6a)`

Answer

A

Explanation

Equation of chord `y = m (x+6a)`
`rArr (y-mx)/(6am) =1`
Homogenizing with the parabola
`y^(2) - 4ax ((y-mx)/(6am)) =0`
`rArr 4amx^(2) + 6amy^(2) -4axy =0`
Now, `tan 45^(@) = |(2sqrt(4a^(2)-24a^(2)m^(2)))/(4am+6am)|`
`rArr 100 a^(2)m^(2) = 4(4a^(2) -24 a^(2)m^(2))`
`rArr 49 m^(2) =4`
`rArr m = +-(2)/(7)`