First slide

Equation of line in Straight lines

Question

The line (p + 2q) x + (p – 3q)y = p – q for different values of p and q passes through the fixed point

Moderate

A

$(\frac{3}{5}, \frac{5}{2})$
B

$(\frac{2}{5}, \frac{2}{5})$
C

$(\frac{3}{5}, \frac{3}{5})$
D

$(\frac{2}{5}, \frac{3}{5})$

Solution

The equation of the given line can be re-written as p(x + y – 1) + q(2x – 3y + 1) = 0 which, clearly, passes through the point of intersection of the lines
x + y – 1 = 0 ------(1)
and 2x – 3y + 1 = 0 -------(2)
for different values of p and q
Solving (1) and (2), we get the coordinates of the point of intersection as $(\frac{2}{5}, \frac{3}{5})$ .

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