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Thiết kế một chóa đèn có mặt cắt hình parabol với kích thước được cho trong hình sau:

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Thực hành 4

Vẽ các parabol sau: a) \({y^2} = 16x\) b) \({y^2} = x\) c) \({y^2} = 32x\)

Phương pháp giải:

Bước 1: Khởi động phần mềm Geogebra Bước 2: Nhập phương trình parabol \({y^2} = 2px\) theo cú pháp y^2 = 2px vào vùng nhập lệnh Bước 3: Quan sát hình vẽ xuất hiện trên vùng làm việc

Lời giải chi tiết:

Thực hiện các bước đã nêu ở phương pháp ta có a) Nhập phương trình parabol theo cú pháp y^2 = 16x vào vùng nhập lệnh ta được hình parabol dưới đây:

 

b) Nhập phương trình parabol theo cú pháp y^2 = x vào vùng nhập lệnh ta được hình parabol dưới đây:

 

c) Nhập phương trình parabol theo cú pháp y^2 = 32x vào vùng nhập lệnh ta được hình parabol dưới đây:

 

Thực hành 5

Thiết kế một chóa đèn có mặt cắt hình parabol với kích thước được cho trong hình sau:

Phương pháp giải:

Bước 1: Giả sử phương trình của parabol Bước 2: Từ kích thước giả thiết cho, xác định điểm nằm trên phương trình Bước 3: Xác định phương trình parabol Bước 4: Sử dụng Geogebra vẽ hình dạng mô phỏng chóa đèn

Lời giải chi tiết:

Chóa đèn có hình dạng parabol nên phương trình mô phỏng chóa đèn có dạng \({y^2} = 2px\)

Gắn hệ tọa độ Oxy ꦕvào chóa đèn với gốc tọa độ tại đỉnh chóa đèn, suy ta phương trình đó đi qua điểm có tọa độ (3; 9)

Thay tọa độ điểm (3; 9) vào phương trình \({y^2} = 2px\), ta có \({9^2} = 2p.3 \Rightarrow p = \frac{{27}}{2}\) Suy ra phương trình mô tả chóa đèn là \({y^2} = 27x\) với \(x \le 3\) Hình ảnh mô phỏng chóa đèn có dạng như hình dưới:

 

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