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

# Find the Equation of a Line Which Passes Through the Point (22, −6) and is Such that the Intercept of X-axis Exceeds the Intercept of Y-axis by 5. - Mathematics

Find the equation of a line which passes through the point (22, −6) and is such that the intercept of x-axis exceeds the intercept of y-axis by 5.

#### Solution

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

Here, a = b + 5            ... (1)
The line passes through (22, −6).

∴$\frac{22}{a} - \frac{6}{b} = 1$            ... (2)

Substituting a = b + 5 from equation (1) in equation (2)

$\frac{22}{b + 5} - \frac{6}{b} = 1$

$\Rightarrow 22b - 6b - 30 = b^2 + 5b$

$\Rightarrow b^2 - 11b + 30 = 0$

$\Rightarrow \left( b - 5 \right)\left( b - 6 \right) = 0$

$\Rightarrow b = 5, 6$

From equation (1)
When b = 5 then, a = 5 + 5 = 10
When b = 6 then, a = 6 + 5 = 11
Thus, the equation of the required line is

$\frac{x}{10} + \frac{y}{5} = 1 or \frac{x}{11} + \frac{y}{6} = 1$

$\Rightarrow x + 2y - 10 = 0 \text { or }6x + 11y - 66 = 0$

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 12 | Page 47