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Let ax+by+c=0 be a variable straight lin...

Let ax+by+c=0 be a variable straight line, where a, b and c are `1^(st), 3^(rd) " and " 7^(th)` terms of an increasing A.P., respectively.
Then prove that the variable straight line always passes through a fixed point and find that point.

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CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
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  3. Let ax+by+c=0 be a variable straight line, where a, b and c are 1^(st)...

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  4. Angle made with the x-axis by a straight line drawn through (1, 2) so ...

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  5. Prove that all the having sum of the intercepts on the axes equal to h...

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  6. Three straight lines 2x+11y - 5 = 0 , 24 x + 7y - 20 = 0 and 4x - 3y ...

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  7. Find the straight line passing through the point of intersection of li...

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  8. Three lines x+2y+3=0,x+2y-7=0,a n d2x-y-4=0 form the three sides of tw...

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  9. Consider a family of straight lines (x+y)+lambda(2x-y+1)=0. Find the...

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  10. Find alpha if (alpha, alpha^2) lies inside the triangle having sides a...

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  11. If 5a+4b+20c=t,then the value of t for which the line ax+by+c-1=0 alwa...

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  12. If the chord y = mx + 1 subtends an angle of measure 45^0 at the major...

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  13. If x/l+y/m=1 is any line passing through the intersection point of the...

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  14. Two sides of a rhombus OABC (lying in the first or third quadrant) of ...

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  15. The equation of straight line belonging to both the families of lines ...

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  16. If m1 and m2 are the roots of the equation x^2-a x-a-1=0 , then the ar...

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  17. Let the algebraic sum of the perpendicular distance from the points (2...

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  18. If the points ((a^3)/((a-1))),(((a^2-3))/((a-1))),((b^3)/(b-1)),(((b^2...

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  19. If a , b ,c are in harmonic progression, then the straight line (x/a)+...

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  20. A variable line cuts n given concurrent straight lines at A1,A2...An s...

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