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In the rectangular coordinate system, the circle with point a (root 3,0) as the center and radius 2 and 3 as the radius intersects the X axis at B, C. and Y axis at D, e.50-
The standard equation of a circle with point a (√ 3,0) as its center and 2 √ 3 as its radius is as follows:
(x-√3)^2+y^2=12
Let x = 0, then: 3 + y ^ 2 = 12,
So y = - 3, y = 3;
Therefore, D and e coordinates are (0, - 3), (0,3) respectively
Let y = 0, then: (x - √ 3) ^ 2 = 12,
So x - √ 3 = 2 √ 3, or - 2 √ 3,
X = 3 √ 3, or x = - √ 3
Therefore, the coordinates of B and C are (3 √ 3,0), (- √ 3,0)
In a rectangular coordinate system, a circle with point a (root 3,0) as its center and 2 and 3 as its radius intersect with X axis at B, C. and Y axis with D, e. (1) if the parabola y = 1 / 3 (1) If the parabola y = 1 / 3, the quadratic power of X + BX + C passes through C, D., find the analytic formula of parabola, and judge whether B is on the parabola (2) If point P is on the symmetry axis of parabola in (1) and the circumference of triangle PBD is minimized, the coordinates of point P are obtained (3) Let Q be a point on the symmetry axis of parabola in (1), whether there is such a point m on the parabola, so that the quadrilateral with B, C, Q, m as the vertex is a parallelogram. If there is, find the M coordinate: if not, please explain the reason
The process is shown in the following figure. (1) B (- v3,0) C (3v3,0) d (- 3,0), e (3,0) is substituted into CD, y = 1 / 3 x ^ 2 - 2 / 3 V3 X - 3 is substituted into B to satisfy the equation, B on the parabola (2) PBD is the smallest, Pb + PD is the smallest, because Pb = PC, it is equivalent to
In the plane rectangular coordinate system, the vertices a (4,0), B (0,4) of △ ABC and point C are on the negative half axis of the X axis, and ∠ BCO = 30 ° BC = 8,
B (0,4), so Bo = 4, ∠ BCO = 30 ° BC = 8, so OC = 4 √ 3, point C is on the negative half axis of X axis, so the C coordinate is (- 4 √ 3,0)
As shown in the figure, the vertex coordinates of △ ABC in the plane rectangular coordinate system are respectively a (2,2) B (0,1) C (1,1). Find out the area of △ ABC
Take BC as the base, pass a as the high ad on BC side, because ad = 1, BC = 1, so s = 1 / 2 * 1 * 1 = 1 / 2
As shown in the figure, put an isosceles RT triangle ABC into a plane rectangular coordinate system so that one vertex C is on the Y axis, and the other vertex B is on the X axis Put an isosceles rtabc into a plane rectangular coordinate system so that one right angle vertex C is on the Y axis and the other right angle vertex B is on the X axis. Report | 2013-01-20 20 20:50 questioner: Xuan Yao Chen | browsing times: 107 times. ① if the distance between P and △ BCO is equal, verify: AP = AC; ② if a (- 2,2) calculates ob + OC value; ③ as shown in the figure, if the distance from P to △ BCO is equal, the three sides are equal, What is the relationship between AP and AC? ④ as shown in the figure, if a (- 1,1), find the value of oc-ob Well, you can draw your own pictures,
Connect Pb and PC ? p to the three sides are equal, ? Pb and PC are angular bisectors BPC = 180 ° - (﹤ CBO + ∠ BCO) / 2 = 135 ° make a circle with a as the center and AC as the radius, ? the center angle of the arc BC pair is ? bac = 90 °, and the circular angle of the arc BC pair is 45 °. (the circumference angle is half of the center angle) ? P point is also on the circle
As shown in the figure, in the plane rectangular coordinate system, the isosceles right triangle ABC is placed at the vertex a of the second quadrant. On the Y axis, the coordinates of the right angle vertex C are (- 1,0), and they will not be indented As shown in the figure, in the plane rectangular coordinate system, the isosceles right triangle ABC is placed on the second quadrant vertex a on the Y axis, and the coordinates of the right angle vertex C are (- 1,0) points B on the parabola y = 1 / 2x2 + 1 / 2x-2 (1) Find AB length (2) Rotate triangle plate ABC by 90 ° anticlockwise around vertex a to reach the position of △ ab1c1 ① Find the route length of point B ② Please judge whether the point B1C! Is on the parabola and explain the reason It's urgent. Give me an answer in a day
If the coordinate of point a is (0, m), then the slope of straight line AC is: m, the slope of straight line BC is: - 1 / m, and the slope of straight line BC is:
1.y=-1/mx-1/m
y=1/2x2+1/2x-2
-1/mx-1/m=1/2x2+1/2x-2
mx2+(m+2)x-4m+2=0
b2-4ac>=0
(m-2)*(m-2)+16m2>=0
M=2
Line BC: y = - 1 / 2x-1 / 2
y=1/2x2+1/2x-2
Coordinates of point B: (- 3,1); coordinates of point A: (0,2), coordinates of C (- 1,0)
AB= root 10, AC= root 5, BC= root 5
(2) Rotate triangle plate ABC by 90 ° anticlockwise around vertex a to reach the position of △ ab1c1
① Find the route length of point B = 0.5 π * root 10
② B1C! On the parabola, now find the straight line
AC1:y=-1/2x+2
y=1/2x2+1/2x-2
X = 2, C1 coordinate: (2,1); a point coordinate: (0,2), AC1 distance = root 5
The slope of line AB = 1 / 3, the slope of Ab1 = - 3,
The line is; y = - 3x + 2
y=1/2x2+1/2x-2
X = 1, or x = 4 (round off); y = - 1, the coordinates of point B1 are; (1, - 1); the coordinates of point A: (0,2)
The length of Ab1 = radical 10, B1C! Is on the parabola
As shown in the figure, in the plane rectangular coordinate system, the coordinates of the three vertices of △ ABC are a (2, 3), B (2, 1), C (3, 2) (1) Judge the shape of △ ABC; (2) If △ ABC is rotated one circle along the line of edge AC, the volume of the rotating body is obtained
(1) Answer: triangle is isosceles right triangle;
From the coordinates of points a, B and C,
AC=
(2-3)2+(3-2)2=
2，
BC=
(3-2)2+(2-1)2=
2，
AB=3-1=2，
Because（
2）2+（
2) 2 = 4 = 22, namely ac2 + BC2 = AB2, AC = BC,
Therefore, the triangle is an isosceles right triangle;
(2) The volume of the cone is 1
3π•BC2•AC=1
3π×（
2）2×
2=2
Three
2π．
As shown in the figure, in the plane rectangular coordinate system, a (1,1) B (5,1) C (1,4) are the three vertices of the triangle ABC. Find the length of BC
Using the translation method, push point a to (0,0), then point B is (4,0), C (0,3) is, AB is 4, AC is 3
Therefore:
BC length 5 should not be a calculation problem. If it is a blank filling problem, you don't even need to draw a picture
In the plane rectangular coordinate system, the coordinates of the three vertices of triangle ABC are a (2,3) B (2,1) C (3,2), so as to judge the shape of triangle ABC
AB = 2 AC = root 2 BC = square of root 2 ab = square of AC + square of BC
The shape of triangle ABC is: isosceles right triangle
As shown in the figure, in the plane rectangular coordinate system, the vertices of triangle ABC are a (0,0), B (4,0), C (3,4) (1) Find the area of triangle ABC; （2） If the triangle ABC is translated upward by 1 unit length to obtain the triangle A1 B1 C1, and then the triangle A1 B1 C1 is translated to the right by 2 unit lengths to obtain the triangle A2 B2 C2, try to draw the triangle A2 B2 C2 in the figure and write out the coordinates of its vertices; (3) What is the relationship between the shape and size of triangle ABC and triangle A2 B2 C2?
(1) Area = 4 * 4 / 2 = 8
（3）A1（0,1）B1（4,1）C1（3,5） A2（2,1）B2（4,3）C2（3,7）
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