The combined equation of three sides of a triangle is `(x^2-y^2)(2x+3y-6)=0` . If `(-2,a)` is an interior point and `(b ,1)` is an exterior point of the triangle, then `2

Options

A. `a in (2,10//3)`
B. `a in (2,10//3)`
C. `b in (-1,9//2)`
D. `b in (-1//1)`

Answer

A, D

Explanation

The sides of the triangle are given by
`(x^(2)-y^(2))(2x+3y-6)=0`
`or," "x-y=0, x+y=0, 2x+3y=0`

We observe than the point `(-2,a)` moves on `x=-2 and (b,1)` moves on y = 1. Thus,
`2 le a le (10)/(3) and -1 le b le 1`