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Giải bài 70 trang 97 SBT toán 10 - Cánh diều

Cho parabol (P) có phương trình chính tắc: y2 = 2px (p > 0) và đường thẳng x = m (m > 0) cắt (P) tại hai điểm I, K phân biệt. Chứng minh hai điểm I và K đối xứng nhau qua trục Ox.

🥀Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho parabol (P) có phương trình chính tắc: y2 = 2px (p > 0) và đường thẳng x = m (m > 0) cắt (P) tại hai điểm I, K phân biệt. Chứng minh hai điểm I và K đối xứng nhau qua trục Ox.

Phương pháp giải - Xem chi tiết

Bước 1: Tham số hóa tọa độ I, K theo PT đường thẳng x = m

Bước 2: Thay tọa độ I, K vào PT (P🍸) và chứng minh tung độ 2 điểm này trái dấu rồi kết luận

Lời giải chi tiết

Do \(I,K \in d:x = m\) nên \(I(m;t),K(m;k)\)Do \(I,K \in (P)\) nên \(\left\{ \begin{array}{l}{t^2} = 2pm\\{k^2} = 2pm\end{array} \right.\)\( \Leftrightarrow {t^2} = {k^2} \Leftrightarrow \left\{ \begin{array}{l}t = k\\t =  - k\end{array} \right.\)

Với t = k thì I và K trùng nhau \( \Rightarrow \) t = k không thỏa mãn

Với t = -k thì I(m ; t) và K(m ; -t). Khi đó I và K đối xứng nhau qua trục Ox (ĐPCM)

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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