The chord PQ of the parabola y 2 = x , where one end P of the chord is at point ( 4 , − 2 ) , is perpendicular to the axis of the parabola. Then the slope of the normal at Q is

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Point P is ( 4 , − 2 ) and PQ ⊥ x -axis So, Q = ( 4 , 2 ) Equation of tangent at ( 4 , 2 ) is ​ y y 1 ​ = 2 1 ​ ( x + x 1 ​ ) ⇒ 2 y = 2 1 ​ ( x + 2 ) ⇒ 4 y = x + 2 ⇒ y = 4 x ​ + 2 1 ​ ​ So, slope of tangent = 4 1 ​ ∴ Slope of normal = − 4

Mathematics - Parabola Question with Solution | TestHub

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