A straight line L with an inclination angle of 45 ° is known to pass through point a (1, - 2) and point B. point B is in the first quadrant, | ab | = 32. (I) calculate the coordinates of point B; (II) if the straight line L and hyperbola C: x2a2 − y2 = 1 (a > 0) intersect at two points E and F, and the midpoint coordinates of line EF are (4,1), calculate the value of A

A straight line L with an inclination angle of 45 ° is known to pass through point a (1, - 2) and point B. point B is in the first quadrant, | ab | = 32. (I) calculate the coordinates of point B; (II) if the straight line L and hyperbola C: x2a2 − y2 = 1 (a > 0) intersect at two points E and F, and the midpoint coordinates of line EF are (4,1), calculate the value of A

(1) The equation of line AB is y = x-3 because the line L with an inclination angle of 45 ° passes through point a (1, - 2) and point B. suppose point B (x, y), we can get y = x − 3 (x − 1) 2 + (y + 2) 2 = 18, because x ＞ 0, y ＞ 0, we can get x = 4, y = 1, so the coordinate of point B is (4,1). (II) we can get the equation of simultaneous line and hyperbola y = x − 3x2a2 − y2 = 1（ 1A2 − 1) x2 + 6x − 10 = 0, let e (x1, Y1), f (X2, Y2), because the midpoint coordinate of the line EF is (4, 1), so X1 + x2 = 6a2a2 − 1 = 8, so a = 2

If the line L passes through the points m (a, 3), n (1,2), and ∈ [- radical 3 / 3 + 1, radical 3 + 1], find the range of inclination angle α of the line L
Is "and a ∈ [(- radical 3 / 3) + 1, (radical 3) + 1]"

If the line L passes through the points m (a, 3), n (1,2), and a ∈ [- √ 3 / 3 + 1, √ 3 + 1], the range of inclination angle α of the line L is obtained
k1=(3-2)/(-√3/3+1-1)
=1/-√3/3=-3/√3=-√3.
k2=3-2)/(√3+1-1)
=1/√3=√3/3.
So α ∈ (- 3, 3 / 3)
That is, α ∈ (- π / 3, π / 6)

If the length of one side of a triangle is 10 and the length of the other side is 5, when the perimeter of the triangle is even, what is the length of the third side of the triangle

The sum of the lengths of any two sides in a triangle is greater than the third side, and the difference between the lengths of any two sides is less than the third side
Let the third side be X
10-XX,5

If the two sides of a triangle are 2 and 6, and the third side is even, the perimeter of the triangle is______ ．

According to the trilateral relationship of a triangle, we can get 6-2 < x < 6 + 2, that is 4 < x < 8. If the length of the third side is even, then x = 6. If the perimeter of the triangle is 2 + 6 + 6 = 14, then the perimeter of the triangle is 14. So the answer is: 14

Given that the lengths of two sides of a triangle are 2 and 5 respectively, and the lengths of the third side are even, then the circumference of the triangle is ()
A. 11b. 13C. 11 or 13D. Uncertain

∵ the lengths of the two sides of the triangle are 2 and 5, respectively, the value range of the third side is 3 ＜ x ＜ 7, the even number that meets the condition is 4 or 6, and the circumference of the triangle is 11 or 13

Given that the lengths of the two sides of a triangle are 7 and 3 respectively, and that the third side is an integer, the probability that the perimeter of the triangle is even is zero______ ．

Let the length of the third side be xcm. Then there is 7-3 ＜ x ＜ 7 + 3, that is, 4 ＜ x ＜ 10. When the length of the third side is an integer, x = 5 or 6 or 7 or 8 or 9. When the perimeter of the triangle is even, x = 6 or 8, then the probability that the perimeter of the triangle is even is 25

It is known that the lengths of two sides of a triangle are 3cm and 5cm respectively, and the circumference is even?
Write clearly
I have another question to ask: Xiaoyi draws four points on the paper. If these four points are connected to form a figure, how many triangles are there in the figure?
Please discuss by category

Pythagorean Theorem 5 square - 3 square = 4 square
The answer is 4cm

If the lengths of the two sides of the triangle are 2cm and 7cm respectively, the value range of the third side length C is______ When the perimeter is even, the length of the third side is______ When the perimeter is a multiple of 5, the third side length is______ ．

According to the triangle trilateral relation theorem, we can get: 7-2 < C < 7 + 2, that is, 5 < C < 9, when the perimeter is even, the third side is 7cm, when the perimeter is a multiple of 5, the third side is 6cm, so the answer is: 5 < C < 9; 7cm; 6cm

The lengths of two sides of a triangle are 2 cm and 9 cm respectively. The length of the third side is an even number. Find the perimeter of the triangle

Let the third side length be a
a9
So 11 > a > 7
The length of the third side is an even number
So a = 8 or a = 10
S=2+9+8=19
Or S = 2 + 9 + 10 = 21

It is known that the lengths of two sides of a triangle are 3cm and 5cm. If the perimeter of the triangle is even, find the third side and perimeter

The value range of the third edge is 5-3