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Intersection of a line and a parabola - class-XI
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The length of the chord of the parabola $y^2 = 4x$ which passes through the vertex and makes $30^o$ angle with x-axis is
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A
$8\sqrt{3}$
💡 Explanation:
The chord passes through the vertex (0,0) and makes 30 degrees with the x-axis, so its equation is y = tan(30)x = x/sqrt(3). Substituting into y^2 = 4x gives x^2/3 = 4x, so x = 12. The length is sqrt(x^2 + y^2) = sqrt(144 + 144/3) = sqrt(144 * 4/3) = 12 * 2/sqrt(3) = 8*sqrt(3).