Question :
Find the equation of the pair of straight lines passing through the point (1, 3) and perpendicular to the lines 2x - 3y + 1 = 0 and 5x + y - 3 = 0
Answer :
First let us first the separate equations of pair of straight lines, and find the product to get the required equation.
Separate equation 1 of the pair of straight lines which is perpendicular to 2x - 3y + 1 = 0
3x + 2y + a = 0
The point (1, 3) lies on the line 3x + 2y + a = 0.
3(1) + 2(3) + a = 0
3 + 6 + a = 0
a = -9
3x + 2y - 9 = 0 -----(1)
Separate equation 2 of the pair of straight lines which is perpendicular to 5x + y - 3 = 0
x - 5y + b = 0
The point (1, 3) lies on the line x - 5y + b = 0.
1 - 5(3) + b = 0
1 - 15 + a = 0
a = 14
x - 5y + 14 = 0 -----(2)
Product of (1) and (2)
(3x + 2y - 9)(x - 5y + 14) = 0
3x2 - 15xy + 42x + 2xy - 10y2 + 28y - 9x + 45y - 126 = 0
3x2 - 13xy - 10y2 + 33x + 72y - 126 = 0
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