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If a, c, b are in AP the family of line ...

If `a, c, b` are in AP the family of line `ax + by + c = 0` passes through the point.

A

a straight line

B

a family of concurrent lines

C

a family of parallel lines

D

None of these

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The correct Answer is:
D
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If a, b, c are in A.P. then the family of lines ax+by+c=0 (A) passes through a fixed point (B) cuts equal intercepts on both the axes (C) forms a triangle with the axes with area = 1/2 |a+c -2b| (D) none of these

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ARIHANT MATHS-THE STRAIGHT LINES-Exercise For Session 3
  1. Locus of the point of intersection of lines x cosalpha + y sin alpha =...

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  2. If a, c, b are in AP the family of line ax + by + c = 0 passes through...

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  3. if the lines x + 2ay + a = 0, x + 3by + b = 0 and x + 4cy + c = 0 are...

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  4. The set of lines ax + by+ c= 0, where 3a+ 2b+ 4c =0, is concurrent at ...

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  5. If the lines ax+y+1=0, x+by+1=0 and x+y+c=0 (a,b and c being distinct ...

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  6. If u=a1x+b1y+c1=0,v=a2x+b2y+c2=0, and (a1)/(a2)=(b1)/(b2)=(c1)/(c2), t...

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  7. The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent...

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  8. If the straight lines x+y-2-0,2x-y+1=0 and a x+b y-c=0 are concurrent,...

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  9. The straight line through the point of intersection of ax + by+c=0 and...

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  10. If the equations of three sides of a triangle are x+y=1, 3x + 5y = 2 a...

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  11. Find the equations of the line through the intersection of 2x - 3y + 4...

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  12. The locus of point of intersection of the lines x/a-y/b=m and x/a+y/b...

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  13. The condition on a and b, such that the portion of the line ax+by-1=0 ...

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  14. If the lines (a-b-c) x + 2ay + 2a = 0 , 2bx + ( b- c - a) y + 2b = 0 a...

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  15. Find the equation of the straight line which passes through the int...

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  16. Let a ,\ b ,\ c be parameters. Then the equation a x+b y+c=0 will repr...

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  17. Prove that the family of lines represented by x(1+lambda)+y(2-lambda)+...

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