The points on the parabola y^2 = 36x whose or | vedclass

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(A) Let the point on the parabola be $(x_1, y_1)$.Given that the ordinate is three times the abscissa,we have $y_1 = 3x_1$.Since the point lies on the

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$(0, 0), (4, 12)$

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(A) Let the point on the parabola be $(x_1, y_1)$.Given that the ordinate is three times the abscissa,we have $y_1 = 3x_1$.Since the point lies on the parabola $y^2 = 36x$,we substitute $y_1$ into the equation:$(3x_1)^2 = 36x_1$$9x_1^2 = 36x_1$$9x_1^2 - 36x_1 = 0$$9x_1(x_1 - 4) = 0$This gives $x_1 = 0$ or $x_1 = 4$.If $x_1 = 0$,then $y_1 = 3(0) = 0$.If $x_1 = 4$,then $y_1 = 3(4) = 12$.Thus,the points are $(0, 0)$ and $(4, 12)$.

The points on the parabola $y^2 = 36x$ whose ordinate is three times the abscissa are

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