ТИПОВОЙ РАСЧЕТ. АНАЛИТИЧЕСКАЯ ГЕОМЕТРИЯ.

Варианты заданий

Часть 1. Аналитическая геометрия на плоскости
1. Заданы вершины треугольника АВС. Требуется
1) составить уравнения сторон АВС; уравнение высоты, опущенной из вершины А на сторону АС; уравнение медианы, проведенной из вершины С.
2) указать для прямой АВ координаты вектора нормали и угловой коэффициент прямой.
3) найти угол между сторонами АС и АВ, расстояние от вершины С до стороны АВ.
4) вычислить периметр треугольника АВС.
2. Построить линии. Указать элементы кривых а)-в).
Часть 2. Аналитическая геометрия в пространстве
3. Найти расстояние от точки 13 EMBED Equation.3 1415 до плоскости, проходящей через три точки: 13 EMBED Equation.3 1415. Построить плоскость.
4. Написать уравнение плоскости, проходящей через точку A, перпендикулярную вектору 13 EMBED Equation.3 1415.
5. Найти угол между плоскостями.
6. Найти координаты точки A, равноудалённой от точек B и C.
7. Написать каноническое уравнение прямой.
8. Найти точку пересечения прямой и плоскости.
9. Нарисовать пространственные линии, заданные пересечением двух поверхностей, установив предварительно, какие это поверхности. В тех случаях, когда это необходимо, привести уравнения поверхностей к каноническому виду.
Вариант №1
1. А(2;-3), В(1;4), С(3;2).
2. а) 2x2+9y2=18; б) 2x2-9y2=18; в) 2x2=-y; г) (x+2)2-(y-3)2=18; д) 2x = 9y2
е) 2x-9y-18=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
9. 13 EMBED Equation.3 1415
Вариант №2
1. А(6;0), В(-2;4), С(3;-4).
2.а) 3x2+8y2=24; б) 3x2-8y2=-24; в) 3x2=-y; г) (x-4)2+(y+1)2=24; д) 3x =8y2;
е) 3x+8y-24=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415

Вариант №3
1.А(0;2), В(1;3), С(-6;-4)
2. а) 5x2+9y2=45; б) 5x2-9y2=-45; в) 5x2=-9y; г) (x-5)2+(y+2)2=45; д) 5x =- 9y2
е) 5x+9y+45=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3
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·4
1.А(3;2), В(-1;4), С(5;7).
2. а) 4x2+7y2=28; б) 4x2-7y2=28; в) 4x2=7y; г) (x-4)2+(y+3)2=28; д) 4x =-7y2
е) 7у-4х=28; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415
Вариант №5
1. A(-1;3), B(2;4), C(1;-5),
2.а) 2x2+7y2=42; б) 2x2-7y2=42; в) 2x2=7y; г) (x+1)2+(y-7)2=21; д) 2x =-7y2
е) 2х-7у+42=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415

Вариант №6
1.А(-2;0), В(2;6) и С(4;2),
2. а) 5x2+8y2=80; б) 5x2-8y2=80; в) 5x=-y2; г) (x-5)2+(y+3)2=10; д) x2 =-8у
е) 5х-8у-40=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415
Вариант №7
1. А(2;-3), В(4;5), С(-1;6).
2. а) 4x2+9y2=36; б) 4x2-9y2=-36; в) 4x2=9y; г) (x-1)2+(y+2)2=8; д) 4x = -y2
е) 3x+2y-6=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 14
·15
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.9. 13 EMBED Equation.3 1415

Вариант №8
1. А(-2;0), В(2;4), С(4;0).
2. а) 2x2+9y2=18; б) 2x2-9y2=18; в) 2x2=-y; г) (x-2)2+(y-1)2=18; д) x = 9y2
е) 2x+9y-18=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415

Вариант №9
1. A(0;2), B(1;-1), C(3;-2),
2.а) x2+4y2=20; б) x2-4y2=-20; в) x2=-4y; г) (x-1)2+(y+2)2=20; д) x =4y2
е) х-4у+20=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415

Вариант №10
1. A(-1;3), B(4;0), C(5;5),
2. а) 6x2+11y2=66; б) 6x2-11y2=-66; в) 6x2=y; г) (x+6)2+(y-3)2=11; д) x =3y2
е) 6х+3у=-12; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415
Вариант №11
1. А(2;-3), В(1;4), С(3;2).
2. а) 2x2+9y2=18; б) 2x2-9y2=18; в) 2x2=-y; г) (x+2)2-(y-3)2=18; д) 2x = 9y2
е) 2x-9y-18=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415

Вариант №12
1.А(6;0), В(-2;4), С(3;-4).
2. а) 3x2+8y2=24; б) 3x2-8y2=-24; в) 3x2=-y; г) (x-4)2+(y+1)2=24; д) 3x =8y2
е) 3x+8y-24=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415

Вариант №13
1.А(0;2), В(1;3), С(-6;-4),
2. а) 5x2+9y2=45; б) 5x2-9y2=-45; в) 5x2=-9y; г) (x-5)2+(y+2)2=45; д) 5x =- 9y2
е) 5x+9y+45=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415
Вариант №14
1.А(3;2), В(-1;4), С(5;7).
2. а) 4x2+7y2=28; б) 4x2-7y2=28; в) 4x2=7y; г) (x-4)2+(y+3)2=28; д) 4x =-7y2
е) 7у-4х=28; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415

Вариант №15
1.A(-1;3), B(2;4), C(1;-5),
2. а) 2x2+7y2=42; б) 2x2-7y2=42; в) 2x2=7y; г) (x+1)2+(y-7)2=21; д) 2x =-7y2
е) 2х-7у+42=0; ж) 13 EMBED Equation.3 1415; з) 13 EMBED Equation.3 1415
3. 13 EMBED Equation.3 1415
4. 13 EMBED Equation.3 1415
5. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415.
6. 13 EMBED Equation.3 1415
7. 13 EMBED Equation.3 1415 13 EMBED Equation.3 1415
8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415

8. 13 EMBED Equation.3 1415; 13 EMBED Equation.3 1415. 9. 13 EMBED Equation.3 1415








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