Find Equation of the Line Passing Through the Point (2, 2) and Cutting off Intercepts on the Axes Whose Sum is 9. - Mathematics

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

The equation of a line in the intercept form is `x/a + y/b = 1` ... (i)

Here, a and b are the intercepts on x and y axes respectively.

It is given thata + b = 9 ⇒ b = 9 – a … (ii)

From equations (i) and (ii), we obtain

If a = 6 and b = 9 – 6 = 3, then the equation of the line is

`x/6 + y/3 = 1 => x +2y - 6 = 0`

If a = 3 and b = 9 – 3 = 6, then the equation of the line is

`x/3 + y/3 = 1 => 2x + y - 6 = 0`

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Chapter 10 Straight Lines
Q 13 | Page 220