its like this

a^{2}b^{2}x^{2} + b^{2}x - a^{2}x -1 = 0

=> b^{2}x ( a^{2}x + 1 ) - 1 ( a^{2}x + 1 ) = 0

=> ( a^{2}x + 1 ) ( b^{2}x - 1 ) = 0

=> x = -1/a^{2} ,or 1/b^{2.}

Ans. 3

centroid will be { ( 2 + 1 + c2) / 3 , ( a + b - 3 ) /3 } , these corodinates are not zero. So none of them will be on x-axis or y-axis.

To get the ordinate on y-axis, a + b = 3

Ans. 1

Let the line segment joining the points ( 2 , - 2 ) and ( 3 , 7 ) be divided by the line 2x + y - 4 = 0 in the ratio k : 1.at pt. P

Therefore coordinates of the point P will be ( 3k + 2 ) / ( k + 1 ) and ( 7k - 2 ) / ( k + 1). But the pt. P lies on the line 2x + Y = 4 also.

Therefore 2 ( 3k + 2 ) / ( k + 1 ) + (7k - 2 ) / ( k + 1 ) = 4

=> 6k + 4 + 7k - 2 = 4k + 4

=> 9k = 2

=> k = 2 / 9. The line segment joining the pts. ( 2, - 2 ) and ( 3, 7 ) is devided by the line 2x + y - 4 = 0 in the ratio 2 : 9