Let ax +by+c=0 be a variable straig...
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Let ax + by + c = 0 be a variable straight line, where a, b and c are 1st, 3rd and 7th terms of some increasing A.P. Then the variable straight line always passes through a fixed point which lies on 

(A) x² + y^2 = 13 

(B) x^2 + y^2 = 5 

(C) y^2 = 9x 

(D) 3x+4y=9

JEE/Engineering Exams
Maths
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Let ax +by+c=0 be a variable straight line, where a, b and c are 1st, 3rd and 7th terms of some increasing A.P. Then the variable straight line always passes through a fixed point which lies on (A) x^2+y^2=13  (B) x^2+y^2=5  (C) y^2=9x  (D) 3x+4y=9
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aIst, b3rd, c7th are in AP a=a b=a+2nd c=a+6d ax+(a+2d)y+(a+bd)=0 a(x+y+1)+d(2y+6)=0 (x+y+1)+da(2y+6)=0 (x+y+1)+λ(2y+6)=0 L1+λL2=0 x+y+1=0    ....1 2y+6=0 y=-3 put y =-3 in 1., x=2  These points satisfy the first equation in question i.e     x2+y2=13 i.e     22+(-3)2=13           4+9=13 13=13

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