If the line 7y - 4x = 10 is a tangent to the | vedclass

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(B) Let the point of contact be $(x_1, y_1)$.The equation of the tangent to the parabola $y^2 = 4ax$ at $(x_1, y_1)$ is $yy_1 = 2a(x + x_1)$.Here,$4a

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$\left( \frac{5}{2}, \frac{7}{2} \right)$

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(B) Let the point of contact be $(x_1, y_1)$.The equation of the tangent to the parabola $y^2 = 4ax$ at $(x_1, y_1)$ is $yy_1 = 2a(x + x_1)$.Here,$4a = 4$,so $a = 1$. The tangent equation is $yy_1 = 2(x + x_1)$,which simplifies to $2x - yy_1 + 2x_1 = 0$.The given line is $4x - 7y + 10 = 0$.Comparing the coefficients of the two equations:$\frac{2}{4} = \frac{-y_1}{-7} = \frac{2x_1}{10}$From $\frac{2}{4} = \frac{y_1}{7}$,we get $y_1 = \frac{14}{4} = \frac{7}{2}$.From $\frac{2}{4} = \frac{2x_1}{10}$,we get $x_1 = \frac{20}{8} = \frac{5}{2}$.Thus,the point of contact is $\left( \frac{5}{2}, \frac{7}{2} \right)$.

If the line $7y - 4x = 10$ is a tangent to the parabola $y^2 = 4x$,find the point of contact.

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