Show that the equation X square - ysquare-x+3y-2=0 represents pair of perpendicular lines and find their equations
Answer (1)
7th Oct, 2020
Hello student!
Let (x - y +c1) and (x+ y +c2) be the required perpendicular lines.
The equations will be a pair of perpendicular lines if it satisfies:-
(x -y)(x + y) + c2(x - y) +c1(x + y) + c1c2 =0
The given equation can thus be written as:-
x^2-y^2-x+3y-2=0-------------------------(i)
=>(x-y)(x+y) + c1(x+y) + c2(x-y) + c1c2=0
=>x^2 - y^2 + (c1+c2)x + (-c2+c1)y + c1c2=0----(ii)
From equation (i) and (ii), we have:-
c1 + c2 = -1and -c2 + c1 = 3
Solving the above two equations, we get:-
2C1 = 2 => c1 = 1 and c2 = -2.
Hence, x - y +1 and x + y - 2 are the required equations of the perpendicular lines.
Hope this would help you:)
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