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Giải bài 7.28 trang 46 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Tìm tiêu điểm và têu cự của elip

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

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

Cho elip \(\left( E \right)\) có phương trình \(\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{16}} = 1\). Tìm tiêu điểm và têu cự của elip

Phương pháp giải - Xem chi tiết

Cho Elip \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) với \(a > b > 0\) có hai tiêu điểm \({F_1}\left( { - c;0} \right),{F_2}\left( {c;0} \right)\)và có tiêu cự là \(2c\) với \(c = \sqrt {{a^2} - {b^2}} \)

Lời giải chi tiết

Ta có: \(\left\{ \begin{array}{l}{a^2} = 36\\{b^2} = 16\end{array} \right. \Rightarrow c = \sqrt {{a^2} + {b^2}}  = 2\sqrt 5 \)Vậy \(\left( E \right)\) có hai tiêu điểm là \({F_1}\left( { - 2\sqrt 5 ;0} \right),{F_2}\left( {2\sqrt 5 ;0} \right)\) và có tiêu cự là \(2c = 4\sqrt 5 \)

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