The vertex A of `DeltaABC` is (3,-1). The equation of median BE and angle bisector CF are x-4y+10=0 and 6x+10y-59=0, respectively. Equation of AC is

Options

A. 5x+18y=37
B. 15x+8y=37
C. 15x-8y=37
D. 15x+8y+37=0

Answer

B

Explanation

Point E is on the median x-4y+10=0.
`therefore E-=(x_(1), (x_(1)+10)/(4))`
Point C is on the bisector 6x+10y-59=0.
`therefore C-=(x_(2), (59-6x_(2))/(10))`
Midpoint of AC is E.
`therefore (x_(2)+3)/(2) = x_(1)`
`rArr x_(2) = 2x_(1)-3 " " (1) `
`"and " ((59-6x_(2))/(10)-1)/(2) = (x_(1)+10)/(4)`
`rArr (49-6(2x_(1)-3))/(20) = (x_(1)+10)/(4)`
`rArr 49-12x_(1)+18 = 5x_(1)+50`
`rArr 17x_(1) = 17`
`therefore x_(1)=1`
Coordinates of E are `(1,(11)/(4))`.
Equation of AC is
`(y+1) = ((11)/(4)+1)/(-2) = (x-3)`
`rArr -8y-8=15x-45`
`rArr 15x+8y=37`