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Planes in 3D

Question

If 5a+5b+20c=t, then the value of t for which the line ax+by+c1=0 always passes through a fixed point is 

Moderate
Solution

Equation of line axc1+byc1+1=0 has two independent parameters.

5a+5b+20c=t

5a+5b=t20c

5ac1+5bc1=t20cc1

R.H.S is independent of c if t=20.



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