A straight line through the point A (3,4) is such that its intercept between the axis is bisected at A. Find its equation.

Options

A. `x+y=7`
B. `3x-4y+7=0`
C. `4x+3y=24`
D. `3x+4y=25`

Answer

C

Explanation

Let the equation of the line be `(x)/(a)+(y)/(b)=1` . It cuts the coordinates axes at P(a,0) and Q(0,b) . It is given that PQ is bisector at A(3,4).
`therefore (a+0)/(2)=3 and (0+b)/(2)=4 implies a=6,b=8`.
Hence, the equation of the line is `(x)/(6)+(y)/(8)=1` or , `4x+3y=24` .