luyện tập phương trình elip 2019

KÍNH CHÀO QUÝ THẦY CÔ
VỀ DỰ GIỜ THĂM LỚP 1OC2!

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II. BÀI TẬP
1. Nhận dạng phương trình đường elip.
Bài tập 1: Phương trình nào là phương trình đường elip trong các phương trình sau?

x y2
a,
+
=1
9 1
2

x2 y 2
b,
+
=1
9 16

2

x
y
c,

+
=1
25 16

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d, x + 4 y = 16
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II. BÀI TẬP
2. Xác định các yếu tố liên quan đến hình dạng elip

Bài tập 2: Xác định độ dài các trục, tiêu cự và tọa độ các đỉnh, các tiêu điểm của elip sau?

x2 y 2
a,
+
=1
16 4
x2 y2
b,

+
=1
25 9

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II. BÀI TẬP
3. lập phương trình chính tắc của elip.
Bài tập 3: Viết phương trình chính tắc của các elip (E) trong các trường hợp sau?

a, (E) có độ dài trục lớn, trục bé lần lượt là 8 và 4
b, (E) có độ dài trục lớn là 10, tiêu cự bằng 6

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Bài tập 4: Một đường hầm xuyên qua núi có chiều rộng là 20 m, mặt cắt đứng của đường hầm có dạng nửa elip. Biết rằng tỉ số

c 1
=
a 2

. Hãy tìm chiều cao của đường hầm đó?

B2
?

A1

O
20

A2


IV. VẬN DỤNG, TÌM TÒI, MỞ RỘNG.

1. Elip và phép co đường tròn
- Elip có thể giãn nở thành hình tròn khi cho tiêu cự c của elip càng nhỏ, tức trục bé của elip
càng gần bằng trục lớn.
- Hình tròn có thể co lại thành elip thông qua phép co hệ số k thích hợp .

Bài tập 5: Bài toán. Trong mặt phẳng tọa độ, cho đường tròn (C ) có
2
2
2
phương trình x  + y  = a  và một số k (0 < k < 1). Với mỗi điểm M(x ;
y) trên (C ), lấy điểm M’(x’ ; y’) sao cho x’ = x và y’ = ky. Tìm tập hợp
các điểm M’.


IV. VẬN DỤNG, TÌM TÒI, MỞ RỘNG.

2/Tính phản xạ của một ellipse có nghĩa là : khi một tia sáng xuất
phát từ một trong hai tiêu điểm của ellipse, nó chiếu tới bề mặt
của ellipse, ngay lập tức nó sẽ phản xạ ra, tia phản xạ này sẽ đi
qua tiêu điểm còn lại. Khái niệm phản xạ trong hình học phẳng có
thể hình dung như sau : gọi tia là đường thẳng d, đường đi khi tới
được ellipse tức sẽ cắt ellipse tại điểm gọi là A. Tại điểm A này, ta

vẽ một đường Ax tiếp xúc với ellipse, sau đó dựng đường vuông
góc Ay vớ Ax. Tia d’ qua A và đối xứng với d qua Ay chính là tia
phản xạ của d. ( xem như 1 BTVN, tự kiểm tra)