In a ` A B C ,A-=(alpha,beta),B-=(1,2),C-=(2,3),` point `A` lies on the line `y=2x+3,` where `alpha,beta` are integers, and the area of the triangle is `S` such that `[S]=2` where `[` .`]` denotes the greatest integer function. Then the possible coordinates of `A` can be `(-7,-11)` (b) `(-6,-9)` `(2,7)` (d) `(3,9)`

Options

A. `a-b=7`
B. `a+b=5`
C. minimum value of the quadratic expression whose zero's are `a` and `b` and leading coefficient is `4` is`-49`
D. minimum value of the quadratic expession whose zero's are `a` and `b` and leading coefficient is `-1` is`49/4`

Answer

A, B, C, D

Explanation

Slope of `AC=(9-3)/(3-2)=6`
Equation of `AC` is`y-3=6(x-2)`
`implies6x-y=9`
But we have equation of `AC` is `ax+by=9`
`impliesa=6,b=-1impliesa+b=5`