Question

If the point (5, 2) bisects the intercept of a line between the axes, then its equation is

पर्याय

•  5x + 2y = 20

•  2x + 5y = 20

• 5x − 2y = 20

•  2x − 5y = 20

Answer 1

 2x + 5y = 20

Let the equation of the line be \[\frac{x}{a} + \frac{y}{b} = 1\]

The coordinates of the intersection of this line with the coordinate axes are (a, 0) and (0, b).
The midpoint of (a, 0) and (0, b) is \[\left( \frac{a}{2}, \frac{b}{2} \right)\]

According to the question:

\[\left( \frac{a}{2}, \frac{b}{2} \right) = \left( 5, 2 \right)\]

\[ \Rightarrow \frac{a}{2} = 5, \frac{b}{2} = 2\]

\[ \Rightarrow a = 10, b = 4\]

The equation of the required line is given below:

\[\frac{x}{10} + \frac{y}{4} = 1\]

\[ \Rightarrow 2x + 5y = 20\]