Consider a variable line `L` which passes through the point of intersection `P` of the lines `3x + 4y = 12` and `x +2y - 5 = 0` meeting the coordinate axes at points `A` and `B.` Then

Options

A. `3x+4y=4xy`
B. `3x+4y=3xy`
C. `4x+3y=4xy`
D. `4x+3y=3xy`

Answer

A

Explanation

Point of intersection of the line
`3x+4y-12=0`
`x+2y-5=0`
is `x=2" and "y=3//2`
(i) Equation of AB is
`(x)/(2h)+(y)/(2k)=1`
`(2)/(2h)+(3)/(4k)=1`
`:." "4k+3h=4khimplies3x+4y-4xy=0` Ans.

(ii) `(k)/(h).(k-(3//2))/(h-2)=-1`
`(k)/(h).(2k-3)/(h-2)=-2`
`2h(h-2)+k(2k-3)=0`
`2(x^(2)+y^(2))-4x-3y=0` Ans.
Here, `a=3h" and "b=3k`
`:." ""equation of AB is "`
`(x)/(3h)+(y)/(3k)=1`
`(2)/(3h)+(1)/(2k)=1`
`3x+4y-6xy=0` Ans.