Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# A Straight Line Passes Through the Point (α, β) and this Point Bisects the Portion of the Line Intercepted Between the Axes. Show that the Equation of the Straight Line is - Mathematics

A straight line passes through the point (α, β) and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is $\frac{x}{2 \alpha} + \frac{y}{2 \beta} = 1$.

#### Solution

The equation of the line with intercepts a and b is $\frac{x}{a} + \frac{y}{b} = 1$

This line intersects the axes at A (a, 0) and B (0, b).
Here, (α, β) is the midpoint of AB.

$\therefore \alpha = \frac{a + 0}{2}, \beta = \frac{0 + b}{2}$

$\Rightarrow a = 2\alpha, b = 2\beta$

Hence, the equation of the line is $\frac{x}{2\alpha} + \frac{y}{2\beta} = 1$

Concept: Straight Lines - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.6 | Q 7 | Page 47