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$T h e p o i n t s (- a, - b), (a, b), (a^{2}, a b) f o r m s$

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a

Vertices of an equilateral triangle

b

Vertices of right angled triangle

c

Vertices of a scalen triangle

d

a striaght line

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detailed solution

Correct option is D

The slope of the line joining the points (a,b), (-a,-b) is b+ba+a=2b2a=baThe slope of the line joining the points (a2,ab), (a,b) is b-aba-a2=b(1-a)a(1-a)=baObserving the above two slopes, they are equal so that the given points are collinear, they forms a straight line

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If the equation of the locus point equidistant from the points $(a_{1}, b_{1})$ and $(a_{2}, b_{2})$ is $(a_{1} - a_{2}) x + (b_{1} - b_{2}) y + c = 0,$ then the value of c is

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