Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

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

Answer in Brief

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 \[\frac{x}{2 \alpha} + \frac{y}{2 \beta} = 1\].

Advertisement Remove all ads

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
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.6 | Q 7 | Page 47
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×