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JEE Main20208 Jan 2020Morning ShiftMathematicsApplication of DerivativesActual

Let the normal at a point P on the curve y 2 - 3 x 2 + y + 10 = 0 intersect the y -axis at 0 , 3 2 . If m is the slope of the tangent at P to the curve, then m is equal to ___________.

Correct answer

0

Step-by-step solution

P ≡ x 1 ,   y 1 2 y y ' - 6 x + y ' = 0 ⇒ y ' = 6 x 1 1 + 2 y 1 ⇒ 3 2 - y 1 - x 1 = - 1 + 2 y 1 6 x 1 ⇒ 9 - 6 y 1 = 1 + 2 y 1 ⇒   y 1 = 1 ∴   x 1 = ± 2 ∴ Slope of tangent = ± 12 3 = ± 4 ∴   n = 4

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