焦半徑考試題及答案

單項(xiàng)選擇題（每題2分，共10題）1.橢圓\(\frac{x^2}{25}+\frac{y^2}{9}=1\)上一點(diǎn)到右焦點(diǎn)的距離為4，則到左焦點(diǎn)的距離為（）A.2B.4C.6D.82.拋物線\(y^2=4x\)上一點(diǎn)到焦點(diǎn)的距離為5，則該點(diǎn)橫坐標(biāo)為（）A.2B.3C.4D.53.雙曲線\(\frac{x^2}{16}-\frac{y^2}{9}=1\)上一點(diǎn)到左焦點(diǎn)的距離為7，則到右焦點(diǎn)的距離為（）A.1B.13C.1或13D.94.橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)\)上一點(diǎn)\(P\)到右焦點(diǎn)距離為\(2c\)，則到左焦點(diǎn)距離為（）A.\(2a-2c\)B.\(2a+2c\)C.\(a-c\)D.\(a+c\)5.拋物線\(x^2=-8y\)上一點(diǎn)到焦點(diǎn)的距離為6，則該點(diǎn)縱坐標(biāo)為（）A.-4B.-5C.-6D.-76.雙曲線\(\frac{y^2}{4}-\frac{x^2}{12}=1\)上一點(diǎn)到下焦點(diǎn)距離為5，則到上焦點(diǎn)距離為（）A.1B.9C.1或9D.77.橢圓\(\frac{x^2}{m}+\frac{y^2}{4}=1\)的焦距為2，則\(m\)的值為（）A.5B.3C.5或3D.88.拋物線\(y=-2x^2\)上一點(diǎn)到焦點(diǎn)的距離為\(\frac{9}{8}\)，則該點(diǎn)縱坐標(biāo)為（）A.-1B.-\frac{1}{2}C.-\frac{3}{4}D.-\frac{5}{4}9.雙曲線\(\frac{x^2}{9}-\frac{y^2}{16}=1\)上一點(diǎn)到右焦點(diǎn)距離為10，則到左焦點(diǎn)距離為（）A.2B.18C.2或18D.1610.橢圓\(\frac{(x-1)^2}{16}+\frac{(y+1)^2}{9}=1\)上一點(diǎn)到右焦點(diǎn)距離為3，則到左焦點(diǎn)距離為（）A.5B.7C.9D.11答案：1.C2.C3.B4.A5.B6.B7.C8.D9.C10.B多項(xiàng)選擇題（每題2分，共10題）1.橢圓\(\frac{x^2}{25}+\frac{y^2}{16}=1\)的焦半徑公式中正確的是（）A.左焦半徑\(r_左=a+ex\)B.左焦半徑\(r_左=a-ex\)C.右焦半徑\(r_右=a+ex\)D.右焦半徑\(r_右=a-ex\)2.拋物線\(y^2=8x\)的焦半徑公式中正確的是（）A.焦半徑\(r=x+2\)B.焦半徑\(r=x-2\)C.焦半徑\(r=y+2\)D.焦半徑\(r=y-2\)3.雙曲線\(\frac{x^2}{9}-\frac{y^2}{7}=1\)的焦半徑公式中正確的是（）A.左焦半徑\(r_左=|ex+a|\)B.左焦半徑\(r_左=|ex-a|\)C.右焦半徑\(r_右=|ex+a|\)D.右焦半徑\(r_右=|ex-a|\)4.橢圓\(\frac{x^2}{m}+\frac{y^2}{n}=1(m>n>0)\)的焦半徑公式可能是（）A.左焦半徑\(r_左=\sqrt{m-n}+e\sqrt{m}x\)B.左焦半徑\(r_左=\sqrt{m-n}-e\sqrt{m}x\)C.右焦半徑\(r_右=\sqrt{m-n}+e\sqrt{m}x\)D.右焦半徑\(r_右=\sqrt{m-n}-e\sqrt{m}x\)5.拋物線\(x^2=-12y\)的焦半徑公式中正確的是（）A.焦半徑\(r=-y+3\)B.焦半徑\(r=-y-3\)C.焦半徑\(r=x+3\)D.焦半徑\(r=x-3\)6.雙曲線\(\frac{y^2}{16}-\frac{x^2}{9}=1\)的焦半徑公式中正確的是（）A.上焦半徑\(r_上=a+ey\)B.上焦半徑\(r_上=a-ey\)C.下焦半徑\(r_下=a+ey\)D.下焦半徑\(r_下=a-ey\)7.橢圓\(\frac{(x+2)^2}{25}+\frac{(y-1)^2}{16}=1\)的焦半徑公式中正確的是（）A.左焦半徑\(r_左=5+\frac{3}{5}(x+2)\)B.左焦半徑\(r_左=5-\frac{3}{5}(x+2)\)C.右焦半徑\(r_右=5+\frac{3}{5}(x+2)\)D.右焦半徑\(r_右=5-\frac{3}{5}(x+2)\)8.拋物線\(y=3x^2\)的焦半徑公式中正確的是（）A.焦半徑\(r=y+\frac{1}{12}\)B.焦半徑\(r=y-\frac{1}{12}\)C.焦半徑\(r=x+\frac{1}{12}\)D.焦半徑\(r=x-\frac{1}{12}\)9.雙曲線\(\frac{(x-1)^2}{4}-\frac{(y+2)^2}{5}=1\)的焦半徑公式中正確的是（）A.左焦半徑\(r_左=|\frac{3}{2}(x-1)+3|\)B.左焦半徑\(r_左=|\frac{3}{2}(x-1)-3|\)C.右焦半徑\(r_右=|\frac{3}{2}(x-1)+3|\)D.右焦半徑\(r_右=|\frac{3}{2}(x-1)-3|\)10.橢圓\(\frac{x^2}{12}+\frac{y^2}{8}=1\)的焦半徑公式中正確的是（）A.左焦半徑\(r_左=2\sqrt{3}+\frac{\sqrt{3}}{3}x\)B.左焦半徑\(r_左=2\sqrt{3}-\frac{\sqrt{3}}{3}x\)C.右焦半徑\(r_右=2\sqrt{3}+\frac{\sqrt{3}}{3}x\)D.右焦半徑\(r_右=2\sqrt{3}-\frac{\sqrt{3}}{3}x\)答案：1.AC2.A3..AD4.AC5.A6.AC7.AC8.A9.AC10.AC判斷題（每題2分，共10題）1.橢圓上一點(diǎn)到兩焦點(diǎn)距離之和為定值（）2.拋物線焦點(diǎn)到準(zhǔn)線距離等于焦半徑（）3.雙曲線右支上一點(diǎn)到左焦點(diǎn)距離大于到右焦點(diǎn)距離（）4.橢圓焦半徑公式與離心率無關(guān)（）5.拋物線焦半徑公式中只與橫坐標(biāo)有關(guān)（）6.雙曲線焦半徑公式中\(zhòng)(e\)越大焦半徑越大（）7.橢圓\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)上一點(diǎn)到左焦點(diǎn)距離一定大于到右焦點(diǎn)距離（）8.拋物線\(y^2=2px\)上一點(diǎn)到焦點(diǎn)距離等于到準(zhǔn)線距離（）9.雙曲線\(\frac{x^2}{m}-\frac{y^2}{n}=1\)焦半徑公式與\(m,n\)無關(guān)（）10.橢圓焦半徑公式在左右焦點(diǎn)情況不同（）答案：1.√2.×3.√4.×5.×6.×7.×8.√9.×10.√簡答題（總4題，每題5分）1.寫出橢圓\(\frac{x^2}{16}+\frac{y^2}{9}=1\)的焦半徑公式。答案：左焦半徑\(r_左=4-\frac{\sqrt{7}}{4}x\)，右焦半徑\(r_右=4+\frac{\sqrt{7}}{4}x\)。2.簡述拋物線\(y^2=6x\)焦半徑公式。答案：焦半徑\(r=x+\frac{3}{2}\)。3.寫出雙曲線\(\frac{x^2}{25}-\frac{y^2}{16}=1\)的焦半徑公式。答案：左焦半徑\(r_左=|\frac{9}{5}x+5|\)，右焦半徑\(r_右=|\frac{9}{5}x-5|\)。4.橢圓\(\frac{(x-3)^2}{25}+\frac{(y+2)^2}{16}=1\)的焦半徑公式是什么？答案：左焦半徑\(r_左=\sqrt{25-16}+\frac{3}{5}(x-3)=3+\frac{3}{5}(x-3)\)，右焦半徑\(r_右=3-\frac{3}{5}(x-3)\)。討論題（總4題，每題5分）1.比較橢圓、拋物線、雙曲線焦半徑公式的異同。答案：橢圓與雙曲線焦半徑公式含離心率等，與曲線性質(zhì)有關(guān)；拋物線焦半徑公式較簡單。橢圓兩焦半徑和為定值，雙曲線有差值關(guān)系，拋物線是到焦點(diǎn)與準(zhǔn)線距離相等。2.如何根據(jù)焦半徑公式求橢圓上點(diǎn)的坐標(biāo)。答案：已知焦半徑，代入焦半徑公式，結(jié)合橢圓方程聯(lián)立求解。如已知左焦半徑，代入左焦半徑公式，再聯(lián)立橢圓方程消元求解\(x,y\)。3.焦半徑公式在解決圓錐曲線問題中有