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Giải bài 51 trang 89 SBT toán 10 - Cánh diều

Trong mặt phẳng toạ độ Oxy, cho đường tròn (C): (x − 3)2 + (y − 4)2 = 25. Tiếp tuyến tại điểm M(0; 8) thuộc đường tròn có một vectơ pháp tuyến là:

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Đề bài

Trong mặt phẳng toạ độ Oxy, cho đường tròn (C): (x − 3)2 + (y − 4)2 = 25. Tiếp tuyến tại điểm M(0; 8)  thuộc đường trওòn 🦂có một vectơ pháp tuyến là:

A. \(\overrightarrow n  = ( - 3;4)\)               B. \(\overrightarrow n  = (3;4)\)                      C. \(\overrightarrow n  = (4; - 3)\)               D. \(\overrightarrow n  = (4;3)\)

Phương pháp giải - Xem chi tiết

Giả sử d là tiếp tuyến tại M của (C). Khi đó \(IM \bot d\) (I là tâm của (C)) nên d nhận vectơ \(\overrightarrow {OM} \) làm VTPT

Lời giải chi tiết

(C) có tâm I(3; 4), bán kính R = 5

Giả sử d là tiếp tuyến tại M của (C) \( \Rightarrow IM \bot d\) \( \Rightarrow \) ♕d nhận \(\overrightarrow {IM} \) làm VTPT

\( \Rightarrow \)\(\overrightarrow {IM}  = ( - 3;4)\)   

Chọn A

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