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AP EAMCET202119 Aug 2021Evening ShiftMathematicsCircleActual

If P ( - 9 , - 1 ) is a point on the circle x 2 + y 2 + 4 x + 8 y - 38 = 0 , then find equation of the tangent drawn at the other end of the diameter drawn through P .

Options

  1. A7 x − 3 y = 60
  2. B7 x − 3 y = 56
  3. C7 x + 3 y = 56
  4. D7 x + 3 y = 60

Correct answer

B. 7 x − 3 y = 56

Step-by-step solution

We have a circle, x 2 + y 2 + 4 x + 8 y - 38 = 0   ⇒ x + 2 2 + y + 4 2 = 58 with centre - 2 ,   - 4 and radius 58 Now, there is a point P - 9 ,   - 1 on the given circle. Let there is a point Q x 1 ,   y 1 on the other end of the diameter drawn through point P . Hence, x 1 - 9 2 = - 2   ⇒   x 1 = 5 and y 1 - 1 2 = - 4 ⇒   y 1 = - 7 So, the other end of the diameter through P is Q 5 ,   - 7 . Now, the slope of the normal to the point Q is the slope of the dia

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