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JEE Main202226 Jun 2022Evening ShiftMathematicsEllipseActual

If m is the slope of a common tangent to the curves x 2 16 + y 2 9 = 1 and x 2 + y 2 = 12 , then 12 m 2 is equal to

Options

  1. A6
  2. B9
  3. C10
  4. D12

Correct answer

B. 9

Step-by-step solution

Given, x 2 16 + y 2 9 = 1 we know that equation of tangent to the ellipse is y = mx ± a 2   m 2 + b 2 y = m x ± 16 m 2 + 9           . . . 1 x 2 + y 2 = 12 Also equation of tangent to the circle is y = m x ± 12 1 + m 2           . . . 2 Now, for common tangent equate eq. 1 and 2 ⇒ 16 m 2 + 9 = 12 1 + m 2 16 m 2 - 12 m 2 = 3 4 m 2 = 3 12 m 2 = 9

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