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Let a x+b y+c=0 be a variable straight l...

Let `a x+b y+c=0` be a variable straight line, whre `a , ba n dc` are the 1st, 3rd, and 7th terms of an increasing AP, respectively. Then prove that the variable straight line always passes through a fixed point. Find that point.

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CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. Show that the straight lines given by x(a+2b)+y(a+3b)=a for different ...

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  2. The straight line 3x+4y-12=0 meets the coordinate axes at Aa n dB . ...

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  3. Let a x+b y+c=0 be a variable straight line, whre a , ba n dc are the ...

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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 lines having the sum of the interceps on the axes e...

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

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

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  8. The lines x+2y+3=0,x+2y-7=0,a n d2x-y-4=0 are the sides of a square. ...

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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. Determine all the values of alpha for which the point (alpha,alpha^2) ...

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  11. If 5a+5b+20 c=t , then find the value of t for which the line a x+b y+...

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  12. If the y=mx+1, of the circle x^2+y^2=1 subtends an angle of measure 45...

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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 entirely in first quadrant or four...

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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. If the algebraic sum of the distances of a variable line from the po...

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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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