If (x_1, y_1) and (x_2, y_2) are the end poin | vedclass

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(C) Given the parabola $y^2 = 4ax$,where $4a = 5$,so $a = \frac{5}{4}$.Let the end points of the focal chord be $(x_1, y_1) = (at_1^2, 2at_1)$ and $(x

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(C) Given the parabola $y^2 = 4ax$,where $4a = 5$,so $a = \frac{5}{4}$.Let the end points of the focal chord be $(x_1, y_1) = (at_1^2, 2at_1)$ and $(x_2, y_2) = (at_2^2, 2at_2)$.For a focal chord,the condition is $t_1t_2 = -1$.Then $x_1x_2 = (at_1^2)(at_2^2) = a^2(t_1t_2)^2 = a^2(-1)^2 = a^2$.Also,$y_1y_2 = (2at_1)(2at_2) = 4a^2(t_1t_2) = 4a^2(-1) = -4a^2$.We need to find $4x_1x_2 + y_1y_2$.Substituting the values: $4(a^2) + (-4a^2) = 4a^2 - 4a^2 = 0$.Since $a = \frac{5}{4}$,the result is $0$.

If $(x_1, y_1)$ and $(x_2, y_2)$ are the end points of a focal chord of the parabola $y^2 = 5x$,then $4x_1x_2 + y_1y_2$ is equal to

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