The combined equation of three sides of a triangle is (x2−y2)(2x+3y−6)=0 such that the points (−2,a) and (b,1) be the interior point and extrerior point of the triangle respectively. If k=[ab], then maximum value of |k| is (where [.] denotes the greatest integer function.)

The combined equation of three sides of a triangle is (x2−y2)(2x+3y�

1.	The combined equation of three sides of a triangle is (x2−y2)(2x+3y−6)=0 such that the points (−2,a) and (b,1) be the interior point and extrerior point of the triangle respectively. If k=[ab], then maximum value of \|k\| is (where [.] denotes the greatest integer function.)
Answer» The combined equation of three sides of a triangle is $(x^{2} - y^{2}) (2 x + 3 y - 6) = 0$ such that the points $(- 2, a)$ and $(b, 1)$ be the interior point and extrerior point of the triangle respectively. If $k = [\frac{a}{b}],$ then maximum value of $\| k \|$ is (where [.] denotes the greatest integer function.)