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AP EAMCET202119 Aug 2021Evening ShiftMathematicsCircleActual

The equations of the tangents to the circle x 2 + y 2 = 4 drawn from the point ( 4 , 0 ) are

Options

  1. Ay = ± 1 3 ( x − 4 )
  2. By = ± 2 3 ( x − 4 )
  3. Cx = ± 1 3 ( y − 4 )
  4. Dx = ± 2 3 ( y − 4 )

Correct answer

A. y = ± 1 3 ( x − 4 )

Step-by-step solution

A line passing through point 4 ,   0 , with slope m is given by y = m x - 4 m     . . . 1   ⇒   m x - y - 4 m = 0 Given, x 2 + y 2 = 4 , Centre 0 ,   0 and Radius = 2 As, the given line is tangent to the circle, hence, the perpendicular distance from the centre to the tangent is equal to the radius of the given circle. - 4 m 1 + m 2 = 2   ⇒   - 4 m 1 + m 2 2 = 4 ⇒ 16 m 2 1 + m 2 = 4 ⇒ m = ± 1 3 So, the equation of the tangent is   y = ±

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