Find the point of contact of the line 2x - y | vedclass

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(A) The equation of the parabola is $y^2 = 16x$. Comparing this with $y^2 = 4ax$,we get $4a = 16$,so $a = 4$. The condition for a line $y = mx + c$ to

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$(1, 4)$

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(A) The equation of the parabola is $y^2 = 16x$. Comparing this with $y^2 = 4ax$,we get $4a = 16$,so $a = 4$. The condition for a line $y = mx + c$ to be tangent to the parabola $y^2 = 4ax$ is $c = a/m$. The given line is $2x - y + 2 = 0$,which can be written as $y = 2x + 2$. Here,$m = 2$ and $c = 2$. Checking the condition: $a/m = 4/2 = 2$,which equals $c$. Thus,the line is indeed a tangent. The point of contact for a tangent $y = mx + c$ to the parabola $y^2 = 4ax$ is given by $(a/m^2, 2a/m)$. Substituting $a = 4$ and $m = 2$: Point of contact = $(4/2^2, 2(4)/2) = (4/4, 8/2) = (1, 4)$.

Find the point of contact of the line $2x - y + 2 = 0$ with the parabola $y^2 = 16x$.

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