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Giải mục 1 trang 54, 55 Chuyên đề học tập Toán 10 - Kết nối tri thức

Cho parabol có phương trình chính tắc \(y = 2px\) (H.3.18).

🧸Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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HĐ1

Cho parabol có phương trình chính tắc \(y = 2px\) (H.3.18). a) Nếu điểm \(M({x_0};{y_0})\) thuộc parabol thì điểm \(N({x_0}; - {y_0})\) có thuộc parabol hay không? b) Từ phương trình chính tắc của parabol, có thể rút ra điều gì về hoành độ của những điểm thuộc parabol?

Lời giải chi tiết:

a) Nếu điểm \(M({x_0};{y_0})\) thuộc parabol thì \({y_0}^2 = 2p{x_0} \Leftrightarrow {( - {y_0})^2} = 2p{x_0}\) nên điểm \(N({x_0}; - {y_0})\) có thuộc parabol. b) Với p>0 thì các điểm thuộc paranol đều có hoành độ \( \ge 0\).  

Luyện tập 1

Trongg mặt phẳng tọa độ Oxy, parabol (P) có phương trình chính tắc và đi qua điểm A(6;6). Tìm tham số tiêu và phương trình đường chuẩn của (P)

Phương pháp giải:

Cho parabol có PTCT  \({y^2} = 2px\) + Tham số tiêu: p + Đường chuẩn: \(\Delta :x =  - \frac{p}{2}\)

Lời giải chi tiết:

Gọi PTCT của (P) là \({y^2} = 2px\) Vì \(A\left( {6;6} \right) \in (P)\) nên \({6^2} = 2.p.6 \Rightarrow p = 3\) + Tham số tiêu: p = 3 + Đường chuẩn: \(\Delta :x =  - \frac{3}{2}\)

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