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 D four

Since the coordinate axes form the two sides of the triangle required,

the triangle is always a right angled triangle.

If $a$ and $b$ are the x-intercept and y-intercept reapectively,

then , $0.5ab=\pm 12\Rightarrow ab=\pm 24$

Thus the answer to the question is $4$

$(+a,+b),(+a,-b),(-a,+b),(-a,-b)$

The equation of the line is

$\frac{x}{a}+\frac{y}{b}=1$ and $ab=24$ . It passes through $(2,3)$

$\frac{2}{a}+\frac{3a}{24}=1$

Solving $a=4$ and $b=6$

Thus the answer to the question is four .

$\frac{x}{4}+\frac{y}{6}=1$

$\frac{x}{4}-\frac{y}{6}=1$

$-\frac{x}{4}+\frac{y}{6}=1$

$-\frac{x}{4}-\frac{y}{6}=1$