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Question

cho (E):

$\frac{x^{2}}{8}+\frac{y^{2}}{4}=1$ va duong thang d:x-

$\sqrt[]{2}y+2=0$ cat (E) tai 2 diem phan biet A,B tim diem C tren (E) sao cho dien tich tam giac ABC lon nhat

thiensugacoi_95 · Answer 1 · 5/31/2013 8:58:22 AM

Vi C thuoc Elip nen thi C co toa do

$(2\sqrt{2}sina; 2cosa)$ dk

$a\in [0;2\pi ]$

De dien tich tam giac la lon nhat thi khoang cach tu C den (d) la lon nhat

Co

$d(C,AB)=\frac{\left| {2\sqrt{2}sina-2\sqrt{2}cosa+2} \right|}{\sqrt{3}}=\frac{\left| {4sin(a-\frac{\pi }{4})+2} \right|}{\sqrt{3}}$

De khoang cach nay lon nhat thi

$sin(a-\frac{\pi }{4})=1<=> a= \frac{3\pi }{4}$

De dang co

$C(2;\sqrt{2})$

Trả lời 31-05-13 08:58 AM

thiensugacoi_95
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