Question

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

• A. One
• B. Two
• C. Three
• D. Four

Answer 1

The correct option is C

Three

(2, 3)

y - 3 = m(x - 2) Area $=\pm 12$

$\frac{1}{2}\left(\frac{2m-3}{m}\right)(3-2m)=\pm 12$

Taking +ve sign, we get Taking –ve sign
$(2m+3{)}^2=0$ $4m^2$ – 36m + 9 = 0
$m=\frac{-3}{2}$ D > 0
therefore, Two values of m
Total 3 values