The number of possible straight lines passing through point(2,3) and forming a triangle with coordiante axes whose area is 12 sq. unit is: a. one b. two c. three d. four

Options

A. one
B. two
C. three
D. four

Answer

C

Explanation

The equation of any line through (2,3) is
y--3=m(x-2)
or y=mx-2m+3
From the figure, the area of `DeltaOAB " is "+-12`, that is,
`(1)/(2)((2m-3)/(m))(3-2m)=+-12`

Taking positive sign, we get `(2m+3)^(2) = 0`. This gives one value of m as -3/2. Taking negative sign, we get
`4m^(2)-36m+9=0(D gt 0)`
This is a quadratic in m which gives two values of m. Hence, three straight lines are possible.