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Giải bài 2 trang 91 SGK Toán 10 tập 2 – Cánh diều

Tìm tâm và bán kính của đường tròn trong môi trường hợp sau:

Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn🌠 - Cánh diều

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

Tìm✨ tâm và bán kính của đường tròn trong môi trường hợp sau:

a) Đường tròn có phương trình\({(x + 1)^2} + {(y - 5ไ)^2} = 9\) ;

b) Đường tròn có phương trình\({x^2♐} + {y^2}ജ-6x - 2y-{\rm{1}}5 = 0\) .

Phương pháp giải - Xem chi tiết

a) Phương trình \({\left( {x - a} \right)^2} + {\left( {y - b} \right)^2} = {R^2}\) có ꧂tâm l꧋à \(I\left( {a;b} \right)\) và bán kính R.

b) Phương trình ൩\({x^2} + {y^2} -🅠 2{\rm{a}}x - 2by + c = 0\) có tâm \(I\left( {a;b} \right)\) và bán kính \(R = \sqrt {{a^2} + {b^2} - c} \).

Lời giải chi tiết

a) Xét \({\left( {x + 1} \right)^2} + {\left( {y - 5} \right)^2} = 9\) \(\Leftrightarrow {\left( {x - ( - 1)} \right)^2} + {\left( {y - 5} \right)^2} = {3^2}\). Ta có a = -1, b = 5, R = 3. Do đó đường tròn có tâm I(-1;5), bán kính R = 3. b) Xét \({x^2} + {y^2} - 6x - 2y - 15 = 0\) \(\Leftrightarrow {x^2} + {y^2} - 2.3.x - 2.1.y + ( - 15) = 0\). Ta có a = 3, b = 1, c = -15,  \(R = \sqrt {{a^2} + {b^2} - c}  = \sqrt {{3^2} + {1^2} - ( - 15)}  = 5\). Do đó đường tròn có tâm I(3;1), bán kính R = 5.

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