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Question

# The number of possible straight lines, passing through (2,3) and forming a triangle with coordinate axes, whose area is 12sq.units, is

A
One
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B
Two
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C
Three
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D
Four
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Solution

## The correct option is C ThreeEquation of any line through (2,3) isy−3=m(x−2)⇒y=mx−2m+3Given, area of ΔOAB is ±12. That is,12(2m−3m)(3−2m)=±12Taking positive sign, we get (2m+3)2=0. This gives one value of m as −32. Taking negative sign, we get 4m2−36m+9=0(D>0)This is a quadratic in m which gives two real values of m.Hence, three straight lines are possible.

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