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If 5a+5b+20 c=t , then find the value of...

If `5a+5b+20 c=t ,` then find the value of `t` for which the line `a x+b y+c-1=0` always passes through a fixed point.

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To solve the problem, we need to find the value of \( t \) for which the line \( ax + by + c - 1 = 0 \) always passes through a fixed point. We start with the given equation: 1. **Given Equation**: \[ 5a + 5b + 20c = t \] 2. **Rearranging the Equation**: ...
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CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. Consider a family of straight lines (x+y)+lambda(2x-y+1)=0 . Find the ...

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

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

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

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

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  6. Two sides of a rhombus OABC ( lying entirely in first quadrant or four...

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

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

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

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

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

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

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  13. Prove that the area of the parallelogram formed by the lines 3x-4y+a=0...

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  14. Two sides of a rhombus lying in the first quadrant are given by 3x-4y=...

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  15. The equation of straight line passing through (-2,-7) and having an in...

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  16. Let A B C be a given isosceles triangle with A B=A C . Sides A Ba n dA...

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  17. A B C is an equilateral triangle with A(0,0) and B(a ,0) , (a>0). L, M...

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  18. Let L1=0a n dL2=0 be two fixed lines. A variable line is drawn through...

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  19. Find the points on y-axis whose perpendicular distance from the line ...

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  20. Find all the values of theta for which the point (sin^2theta,sintheta)...

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