Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x2 + y2 = 5

Question

Prove algebraically that the straight line with equation x = 2y + 5 is
a tangent to the circle with equation x2 + y2 = 5

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Thông Đạt 3 years 2021-08-30T10:34:30+00:00 1 Answers 63 views 0

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  1. RuslanHeatt
    0
    2021-08-30T10:35:52+00:00
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    Answer:

    { \tt{line : x = 2y + 5}} \\ { \tt{circle : {x}^{2} + {y}^{2} = 5}} \\ substitute \: line \: in \: circle \\ { \tt{ {(2y + 5)}^{2} + {y}^{2} = 5 }} \\ { \tt{4 {y}^{2} + 20y + 25 + {y}^{2} = 5}} \\ { \tt{5 {y}^{2} + 20y + 20 = 0 }} \\ { \tt{ {y}^{2} + 4y + 4 = 0 }} \\ y = - 2 \\ x = 2( - 2) + 5 = 1 \\ { \tt{centre = ( - 1, \: 2)}} \\ { \tt{radius = 5 \: units}} \\ hence \: proved

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )