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Find the area of the quadrilateral forme...

Find the area of the quadrilateral formed by common tangents drawn from a point P to the circle `x^(2) + y^(2) = 8` and the parabola `y^(2) =16x`, chord of contact of tangents to the circle and chord of contact of tangents to the parabolas.

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To find the area of the quadrilateral formed by the common tangents drawn from a point P to the circle \(x^2 + y^2 = 8\) and the parabola \(y^2 = 16x\), we will follow these steps: ### Step 1: Identify the parameters of the circle and parabola - The equation of the circle is \(x^2 + y^2 = 8\). The center is at (0, 0) and the radius \(r = \sqrt{8} = 2\sqrt{2}\). - The equation of the parabola is \(y^2 = 16x\). Here, \(4a = 16\) implies \(a = 4\). ### Step 2: Find the equation of the tangent to the parabola The equation of the tangent to the parabola \(y^2 = 4ax\) at point \((x_1, y_1)\) is given by: ...
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