The area of the triangle formed by the coordinate axes and a line is 6 square units and the length of the hypotenuse is 5 units . Find the equation of the line
Let the line cut the x-axis and the y-axis at A(a, 0) and B(0, b) respectively.
∴OA = a
OB = b
Area of the ΔOAB = =6
=> ab = 12
AB is the hypotenuse of the right ΔOAB.
From equations (1) and (2) , we get
a = 4
b = 3
Hence, the equation of the line AB is
If we take the negative values of the square roots in (1) and (2), we get
a = - 4
b = - 3
then the equation of the line AB is