Angle between tangent drawn from the point P(1, – 1) to the circle x2 + y2 + 8x + 6y = 0 is

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Angle between tangent drawn from the point P(1, – 1) to the circle x2 + y2 + 8x + 6y = 0 is

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Ariana 4 weeks 2021-09-22T21:59:51+00:00 1 Answer 0 views 0

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    2021-09-22T22:01:19+00:00

    Given : point P(1, – 1) and circle x2 + y2 + 8x + 6y = 0 is

    To find : Angle between tangent drawn from the point P(1, – 1)

    Solution:

    x² + y² + 8x + 6y = 0

    => (x + 4)² – 16 + (y + 3)² – 9 = 0

    => (x + 4)² + (y + 3)² = 25

    => (x + 4)² + (y + 3)² = 5²

    => Center = – 4 ,  – 3

       Radius =  5

    Distance Between P (1 , – 1)  & center  (-4 ,3 )

    = √(-4 – 1)² + (3 -(-1))²

    = √25 + 16

    = √41

    2x is the angle  between tangent drawn from the point P(1, – 1) to the circle x²² + y² + 8x + 6y = 0 is

    Sin x  =  5/√41

    x =Sin⁻¹(5/√41)

    => x = 51.34°

    => 2x = 102.68°

    Angle between tangent drawn from the point P(1, – 1) to the circle x² + y² + 8x + 6y = 0 is  102.68°

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