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Question

The combined equation of three sides of a triangle is (x2−y2)(2x+3y−6)=0. lf (−2,a) and (b,1) are interior points of the triangle, then

A
2<a<103
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B
2<a<103
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C
1<b<92
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D
1<b<1
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Solution

The correct options are
C 2<a<103
D 1<b<1
The figure shows the triangle enclosed by three lines x+y=0,xy=0,2x+3y6=0
The line X=2 will cut x=y at (2,2), and the line 2x+3y6=0 at (2,103)
From the figure, all the points on x=2, between these two points, will be interior points of the triangle.
Hence, 2<a<103
Similarly the line y=1 cuts x=y at (1,1), and the line x=y at (1,1).
From the figure, all the points on y=1, between these two points, will be interior points of the triangle.
Hence, 1<b<1
160671_34802_ans.png

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