If one end of a focal chord of the parabola 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 $a = 4$.Let the coordinates of the ends of the fo

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$(16, 16)$

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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 $a = 4$.Let the coordinates of the ends of the focal chord be $(at_1^2, 2at_1)$ and $(at_2^2, 2at_2)$.For a focal chord,the relation between the parameters is $t_1 t_2 = -1$.Given one end is $(1, -4)$,we have $2at_1 = -4$.Substituting $a = 4$,we get $2(4)t_1 = -4$,which gives $t_1 = -1/2$.Since $t_1 t_2 = -1$,we have $t_2 = -1 / t_1 = -1 / (-1/2) = 2$.The other end is $(at_2^2, 2at_2) = (4(2)^2, 2(4)(2)) = (4 	imes 4, 16) = (16, 16)$.

If one end of a focal chord of the parabola $y^2 = 16x$ is $(1, -4)$,find the other end.

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