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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 Three
Equation of any line through (2,3) is
y3=m(x2)
y=mx2m+3
Given, area of ΔOAB is ±12. That is,
12(2m3m)(32m)=±12
Taking positive sign, we get (2m+3)2=0. This gives one value of m as
32.

Taking negative sign, we get
4m236m+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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