if a straight lined joining origin to the points of intersection of the line x+y=1 with the curve x^2+y^2+x-2y-m=0 are perpendicular to each other,thenthe value of m should be
Answer (1)
16th Dec, 2019
Substituting 'y = 1-x' in the equation of given curve, we will get a quadratic equation in 'x' whose both roots (say, x1 and x2) has a product equal to (1-m)/2.
Again substituting 'x = 1-y' in the equation of given curve, we will get a quadratic equation whose roots (say, y1 and y2) has product equal to (2-m)/2.
Given, both the lines are perpendicular i.e., the product of their slopes is (-1).
=> ((y1)*(y2))/((x1)*(x2)) = -1
=> (2-m)/(1-m) = -1
=> 2-m = m-1
=> m = 3/2
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