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If the equation of the tangent at the point P 3,4 on the parabola whose axis is the x -axis is 3 x - 4 y + 7 = 0, then the distance of the tangent from the focus of the parabola is

Correct answer

2.5

Step-by-step solution

Slope of the tangent is 3 4 = tan ⁡ θ Slope of the focal chord through P 3,4 is tan ⁡ 2 θ = 2 tan ⁡ θ 1 - t a n 2 θ i.e. tan 2 θ = 2 3 4 1 - 9 16 = 24 7 Equation of the focal chord through P is y - 4 = 24 7 x - 3 Focus is S 11 6 , 0 Distance of the focus from the tangent is 3 11 6 - 4 0 + 7 3 2 + 4 2 = 5 2 = 2 . 5

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