Prove that the area of the traingle formed by the tangents drawn from `(x_1,y_1)` to `y^2=4ax` and their chord of contact is `(y_1^2-4ax_1)^(3//2)//2a`.

Options

A. `((y_(1)^(2)+4ax_(1))^("3/2"))/(2a)`
B. `((y_(1)^(2)-4ax_(1))^("3/2"))/(2a)`
C. `((y_(1)^(2)+4ax_(1))^("3/2"))/(a)`
D. none of these

Answer

B

Explanation

From illustration 3 we have
Area of `DeltaPQR`
`=1/2(QR)xx["Length of the parependicular from "(x_(1), y_(1)) "on QR"]`
`=1/2xx1/4sqrt((y_(1)^(2)-4ax_(1))(y_(1)^(2)+4a^(2)))xx{(y_(1)^(2)-2a(x_(1)xxx_(1)))/(sqrt(y_(1)^(2)+4a^(2)))}`
`1/(2a)(y_(1)^(2)-4ax_(1))^("3/2")`