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Q1if a,b,c are the three terms of AP then prove that the line ax+by+c=0 always passes through a fixed point.
Q2if a,b,c are the three terms of GP then prove that the line ax+by+c=0 always forms a triangle with axes of constant area.
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3 Answers
1Q1
Apply the condition of AP, i.e 2b=a+c
or a-2b+c=0
implies the line ax+by+c=0 always passes through (1,-2).
1Q2
Line ax+by+c=0 have
x-intercept= -c/a
y-intercept= -c/b
therefore area of triangle formed= 1/2*(-c/a)*(-c/b)
=1/2*c2/ab
now since b=a*r and c=a*r2 (r being common ratio)
Area=1/2*r3
which is constant as r is constant