P(a, b) is the mid-point of a line segment ...

NCERT Class XI Mathematics - Straight Lines - Solutions

Question : 32 of 74

Marks: +1, -0

P(a, b) is the mid-point of a line segment between axes. Show that equation of the line is

\frac{x}{a}+\frac{y}{b}

= 2

Solution:

Let the line AB makes intercepts c and d on the x-axis and y-axis respectively.

∴ A(c, 0) and B(0, d).

Let P(a, b) be the midpoint of AB.

Then

\frac{c+0}{2}

= a and

\frac{0+d}{2}

= b

⇒ c = 2a and d = 2b

So, the required equation is

\frac{x}{2a}+\frac{y}{2b}

= 1 ⇒

\frac{x}{a}+\frac{y}{b}

= 2

Go to Question:

Prev Question

Next Question