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(B) The area of the triangle formed by the tangents from a point $(x_1, y_1)$ to the parabola $y^2 = 4ax$ and their chord of contact is given by the f

Vedclass · Accepted Answer

$2$

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(B) The area of the triangle formed by the tangents from a point $(x_1, y_1)$ to the parabola $y^2 = 4ax$ and their chord of contact is given by the formula: $	ext{Area} = \frac{(y_1^2 - 4ax_1)^{3/2}}{2a}$.Given the parabola $y^2 = 8x$,we have $4a = 8$,so $a = 2$.The point is $(x_1, y_1) = (4, 6)$.Substituting these values into the formula:$	ext{Area} = \frac{(6^2 - 4(2)(4))^{3/2}}{2(2)}$$	ext{Area} = \frac{(36 - 32)^{3/2}}{4}$$	ext{Area} = \frac{(4)^{3/2}}{4}$$	ext{Area} = \frac{8}{4} = 2$.

What is the area of the triangle formed by the tangents drawn from the point $(4, 6)$ to the parabola $y^2 = 8x$ and their chord of contact?

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