Who knows how to find the area of ellipse? Area formula

Area of ellipse
Figure 3-7 shows that O is the center of the ellipse, a, a ', B and B' are the "vertex", AA 'is the "major axis", BB' is the "minor axis"
In addition, the long OA = a is called "long radius", and the short ob = B is called "short radius"
There are also ellipses called "oblong"
When a = B, an ellipse is a circle
When the area of an ellipse is denoted as s, the area of an ellipse can be calculated by the formula s = π ab. when a = B, of course, s represents the area of a circle
When long radius a = 3 (CM) and short radius B = 2 (CM), its area s = 3 × 2 × π = 6 π (cm 2)
In the examples so far, such as the length of the circle, the length of the arc, the area of the circle, the area of the sector, the area of the bow, the area of the ellipse, etc., all use the PI
In this way, π is not only an indispensable number for calculating circles, but also ellipses

The geometric figure of the area formula of the inverted circle

S 〓 3.14 × square of radius of circle
Cut the circle into small pieces of paper. The small pieces of paper can be put together into an approximate parallelogram. They can also be triangles. Trapezoids are pushed out in this way

A problem of analytic geometry in Senior High School
If 2x1-3y1 = 4, 2x2-3y2 = 4, then the linear equation through two points a (x1, Y1), B (X2, Y2) is___

y=2/3x-4/3

When the line x + 2y-2 = 0 is rotated 90 ° anticlockwise around the origin, the linear equation is______ ．

A straight line x + 2y-2 = 0 passes through two points (2,0), (0,1), and rotates it 90 ° counterclockwise around the origin of the coordinate to get the coordinates of the corresponding points as (0,2), (- 1,0). If the analytical formula of the straight line passing through these two points is y = KX + B, then B = 2 − K + B = 0, the solution is k = 2, B = 2, that is, the analytical formula of the rotated line is y = 2x + 2, that is, 2x-y + 2 = 0. So the answer is: 2x-y + 2 = 0

Two solutions to analytic geometry problems in Senior High School
1. The intercept of line L on two coordinate axes is equal, and the distance from P (4,3) to line L is 3 times the root sign 2
2. In △ ABC, a (4,5), B are on the x-axis, C is on the line L: 2x-y + 2 = 0, find the minimum perimeter of △ ABC, and find the coordinates of B and C
Please attach the process

1.
K = 1, let y = x + B, the absolute value / root of (1-B) 2 = 3 times root 2, B = - 5 or 7
y=x+7,y=x-5
two
First fix point B, make D (- 1.6,5.8) of symmetry point a about 2x-y + 2 = 0, take the minimum value of point C = AB + BD, then make e (4, - 3) of symmetry point a about X axis, and the value is less than or equal to de

In the equilateral triangle ABC with side length 2a, the sum of the distances from a point P to AB and AC is equal to twice the distance from it to the third side. Try to find the trajectory equation of point P

d1+d2=2d3
2a*d1+2a*d2=2*2a*d3
S triangle PAB + s triangle PAC = 2S triangle PBC
Then s triangle PBC = 1 / 2 * s triangle ABC
Then the height of the equilateral triangle ABC whose distance from P to BC is 1 / 2
P is on the median line of the triangle with BC as the base

A high school analytic geometry problem
Given the circle O: x2 + y2 = 4, the point P is a moving point on the line L: x = 4
1) If the length of tangent from P to circle O is 2 3, the coordinates of point P and the length of arc between two tangents are obtained
2) If the point a (- 2,0) B (2,0), the other intersection points of the line PA, Pb and the circle O are m, n respectively, we prove that the line nm passes through (1,0)

Suppose that the tangent point from P to circle O is Q, then OQP is a right triangle, OQ = 2, QP = 2, root sign 3. OP = 4;
2. The vertical lines of M, n to L are

If the line and ellipse are known, the coordinate of intersection point can be calculated by chord length formula
3x+10y-25=0
x²/25+y²/4=1

The chord length is 0, and there is only one intersection (3,8 / 5)

What are the chord length formulas of a circle

1. Chord length = 2rsina
R is the radius and a is the center angle
2. Arc length L, radius r
Chord length = 2rsin (L * 180 / π R)

What is the chord length formula of the tangent circle of a straight line?

Chord length = │ x1-x2 │ √ (k ^ 2 + 1) = │ y1-y2 │ √ [(1 / K ^ 2) + 1]
Where k is the slope of the straight line, (x1, Y1), (X2, Y2) are the two intersection points of the straight line and the curve, "│" is the absolute value sign and "√" is the root sign

Who knows how to find the area of ellipse? Area formula