Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

3

Answer 2

Equation of line $\frac{x}{a}$+ $\frac{y}{b}$= 1, through (2, 3)

Ю $\frac{2}{a}$+ $\frac{3}{b}$= 1 Ю 2b + 3a = ab

area = $\frac{1}{2}$|ab| = 12

|ab| = 24 Ю ab = ± 24

When ab = 24

2b + 3a = 24

Ю 2ab + 3a² = 24a

Ю 3a² – 24a + 48 = 0

Ю a² – 8a + 16 = 0

Ю a = 4 Ю b = 6

When ab = –24

Ю 2b + 3a = –24

Ю a² + 8a – 16 = 0

Two values of a

Hence 3 straight lines