How to draw conic instead of conic with Geometer's Sketchpad

How to draw conic instead of conic with Geometer's Sketchpad

First use tools to draw an ellipse, preferably one with horizontal axis or vertical axis, then take any point on the vertical axis, then take any point on the ellipse, connect the two points, select the line segment and the point on the ellipse, and click "structure → track" with the mouse. Then hide the unnecessary things

3-2 / X-2 > 3 / x + 1 to solve linear inequality of one variable

3-（X-2）/2>（x+1）/3
3-X+1>X/3+1/3
4X/3＜ 4-1/3
4X/3＜ 11/3
X＜ 11/4.

Let m, M + 1 and M + 2 be the lengths of the three sides of an obtuse triangle, then the value range of the real number m is ()
A. 0＜m＜3B. 1＜m＜3C. 3＜m＜4D. 4＜m＜6

If m, M + 1 and M + 2 are the lengths of the three sides of an obtuse triangle, and the obtuse angle of the largest pair of sides m + 2 is α, then cos α = M2 + (M + 1) 2 − (M + 2) 22m (M + 1) = m − 3M ＜ 0 and 0 ＜ m ＜ 3 can be obtained from the cosine theorem. Then M + m + 1 ＞ m + 2 and 〈 m ＞ 1 can be obtained according to the sum of any two sides is greater than the third side

Given the quadratic function y = x & sup2; - x + 8 / 1, when the independent variable x takes m, the corresponding function value is less than 0; when the independent variable x takes M-1, M + 1, the corresponding function value is less than 0,
The corresponding function values are Y1 and Y2. How to calculate that Y1 is greater than 0 and Y2 is greater than 0

It should be y = x & # 178; - x + 1 / 8, that is, y = (x-1 / 2) &# 178; - 1 / 8
The opening of the function is upward, the zero point is in (0,1), and the value of the function outside the interval is greater than 0
When x is m, the corresponding function value is less than 0, then 0

The fourth power of X + the fourth power of Y + the fourth power of Z - the second power of 2x - the second power of 2x, the second power of Z + the second power of 2Y
Factorization

(X^2-Y^2-Z^2)^2

Put 100 pieces on the four sides of the square. There should be one on each corner. The number of pieces on each side should be equal. There should be () pieces on each side

26

Please match the quadratic function y = ½ X & #178; - x + 2 into the form of y = a (x-m) ² + n,

y=½x²-x+2=1/2(x^2-2x)+2
=1/2(x^2-2x+1-1)+2
=1/2(x-1)^2+3/2

It is known that the inverse proportion function y = K / X and the primary function y = 4x-4, where the passing point of the primary function (k, - 8) (1) try to find the analytic expression of the inverse proportion function (2) if there is a point a on the above two function images at the same time, find the coordinates of point a (3) find the length of OA

1, the linear function y = 4x-4 passes through the point (k, - 8), so - 8 = 4k-4, k = - 1. The analytic expression of inverse proportional function is y = - 1 / x 2. Substituting y = - 1 / x into y = 4x-4, we get (2x-1) ^ 2 = 0, x = 1 / 2, y = - 2, so the coordinate of point a is (1 / 2, - 2) 3, and the length of OA = (root 17) / 2

Decomposition factor: A3 power, b-2a power, B2 power + B3 power

Power A3, power b-2a2, power B2 + power AB3
=ab(a²-2ab+b²)
=ab(a-b)²

For △ ABC, △ Abe and △ ACD are made on the outside of △ ABC with AB and AC as sides respectively, so that ab = AE, AC = ad, and ∠ BAE = ∠ CAD, BD and CE intersect at point H
When ∠ BAE = 60 ° the verification is: he = HA + Hb

It is proved that if EF = BH and AF are intercepted on EH, because ∠ BAE = ∠ CAD, so ∠ EAB + ∠ BAC = ∠ CAD + ∠ BAC, that is ∠ EAC = ∠ bad and AE = AB, AC = ad, so △ AEC ≌ abd, so ∠ AEC = ∠ abd, because AE = AB, EF = BH, so △ AEF ≌ ABH, so AF = ah, ∠ EAF = ∠ bah, because ∠ EAF + ∠ Fab = 60