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Let a focal chord of the parabola y^2=16x be at a perpendicular distance of 2 units from the vertex. The length of this focal chord is _______

Correct answer

64

Step-by-step solution

The equation of the given parabola is y^2 = 16x , which is of the form y^2 = 4ax . Here, 4a = 16 a = 4 . Let the focal chord make an angle with the positive x-axis. The equation of the focal chord passing through the focus (a, 0) is: y - 0 = (x - a) x - y - a = 0 The perpendicular distance p of this chord from the vertex (0,0) is given by: p = |0 - 0 - a | ^2 + 1 = a | | | | = a | | Given that p = 2 and a = 4 : 4 | | = 2 | | = 1 2 cosec ^2 = 4 The length of a focal chord is given by the formula L = 4a cosec ^2 . Su

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