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JEE Main20231 Feb 2023Evening ShiftMathematicsParabolaActual

If the x -intercept of a focal chord of the parabola y 2 = 8 x + 4 y + 4 is 3 , then the length of this chord is equal to _____ .

Correct answer

0

Step-by-step solution

Given, The x -intercept of a focal chord of the parabola y 2 = 8 x + 4 y + 4 is 3 , Now simplifying equation of the given parabola we get, y 2 = 8 x + 4 y + 4 ⇒ y - 2 2 = 8 x + 1 Now on comparing with standard parabola y 2 = 4 a x we get, a = 2 ,   X = x + 1 ,   Y = y - 2 Hence, the vertex is - 1 , 2 and focus is 1 , 2 So, equation of line passing through focus is given by y - 2 = m x - 1 Now, putting 3 , 0 as given x - intercept of focal chord is 3 in the above line we get, m = - 1 So, equation of

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