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AP EAMCET20224 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

The number of those tangents to the curve y 2 - 2 x 3 - 4 y + 8 = 0 which pass through the point 1 , 2 is

Options

  1. A0
  2. B2
  3. C1
  4. D3

Correct answer

B. 2

Step-by-step solution

Let P α , β be any point on the curve y 2 - 2 x 3 - 4 y + 8 = 0 Now, 2 y d y d x - 6 x 2 - 4 d y d x = 0 ⇒    2 y - 4 d y d x - 6 x 2 = 0 ⇒    d y d x = 6 x 2 2 y - 4 Thus, slope = m = d y d x P = 6 α 2 2 β - 4 Now, the equation of the tangent at P is y - β = 6 α 2 2 β - 4 x - α which is passing through 1 , 2 ⇒    2 - β = 6 α 2 2 β - 4 1 - α ⇒    2 - β = 3 α 2 β - 2 1 - α &

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