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AP EAMCET201825 Apr 2018Morning ShiftMathematicsApplication of DerivativesActual

If 5 x - 2 y + k = 0 is a tangent to the parabola y 2 = 6 x , then their point of contact is

Options

  1. A6 5 , 6 5
  2. B6 5 , 6 25
  3. C6 25 , 6 5
  4. D6 25 , 6 25

Correct answer

C. 6 25 , 6 5

Step-by-step solution

y 2 = 6 x ⇒ 2 y d y d x = 6 ⇒ d y d x = 3 6 x → slope of tangent Also, 5 x - 2 y + k = 0 ⇒ y = 5 2 x + k 2 Comparing with the standard form of line in slope intercept form, we get m = 5 2 → slope Therefore, 3 6 x = 5 2 ⇒ 3 2 × 3 · x = 5 2 ⇒ 3 x = 5 2 ⇒ x = 6 5 ⇒ x = 6 25 And, y = 6 5 . Hence, point of contact is 6 25 , 6 5 .

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