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(D) The equation of the parabola is $y^2 = 4x$, so $a = 1$. The point from which tangents are drawn is $(x_1, y_1) = (-1, 2)$. The equation of the cho

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(D) The equation of the parabola is $y^2 = 4x$, so $a = 1$. The point from which tangents are drawn is $(x_1, y_1) = (-1, 2)$. The equation of the chord of contact is $yy_1 = 2a(x + x_1)$, which becomes $y(2) = 2(1)(x - 1)$, or $y = x - 1$. Rearranging, we get $x - y - 1 = 0$. The length of the chord of contact is given by $\frac{2}{a} \sqrt{(y_1^2 - 4ax_1)(a^2 + y_1^2)} = \frac{2}{1} \sqrt{(4 - 4(1)(-1))(1^2 + 2^2)} = 2 \sqrt{(8)(5)} = 2 \sqrt{40} = 4\sqrt{10}$. The perpendicular distance $h$ from the point $(-1, 2)$ to the line $x - y - 1 = 0$ is $h = \frac{|-1 - 2 - 1|}{\sqrt{1^2 + (-1)^2}} = \frac{4}{\sqrt{2}} = 2\sqrt{2}$. The area of the triangle formed by the tangents and the chord of contact is given by $\frac{(y_1^2 - 4ax_1)^{3/2}}{2a} = \frac{(4 - 4(1)(-1))^{3/2}}{2(1)} = \frac{8^{3/2}}{2} = \frac{16\sqrt{2}}{2} = 8\sqrt{2}$.

From the point $(-1, 2)$, tangents are drawn to the parabola $y^2 = 4x$. The area of the triangle formed by the chord of contact and the tangents is: (in $\sqrt{2}$)

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