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Prove that the curves `y^2=4xa n dx^2+y^2-6x+1=0`touch each other at the point (1,2). |
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Answer» We have, `y^(2)=4x` and `x^(2)+y^(2)-6x+1=0` Since, both the curves touch each other at (1,2) i.e., curves are passing through (1,2). `therefore 2y.(dy)/(dx)=4` and `(dy)/(dx) = 4/(2y)` and `(dy)/(dx)= (6-2x)/(2y)` `rArr (dy)/(dx)_(1.2) = 4/4=1` and `(dy)/(dx)_(1/2) = ((6-2).1)/(2.2) = 4/4=1` `rArr m_(1)=1` and `m_(2)=1` Thus, we see that slope of both the curves are equal to each other i.e, `m_(1)=m_(2)=1` at the point (1.2). Hence, both the curves touch each other. |
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