F1 and F2 are the two focal points of hyperbola, F1 is the focal point of parabola y ^ 2 = 4x, hyperbola passes a (- 2,0), B (2,0), find the trajectory equation of F2 Note the explanation of the value range of X Don't you know what to do?

From the problem, the focus formula has F1 over (1,0), hyperbola C = 1, so
X ^ 2 / A ^ 2 - y ^ 2 / b ^ 2 = 1, substituting a, B two points have a ^ 2 = 4, obviously a ^ 2 > C ^ 2,
So this hyperbola doesn't exist

Let p be a moving point on hyperbola x24-y2 = 1, o be the origin of coordinates, and m be the midpoint of line OP, then the trajectory equation of point m is______ ．

Let m (x, y), then p (2x, 2Y) be substituted into hyperbolic equation to obtain x2-4y2 = 1, which is the trajectory equation of point m x2-4y2 = 1. Answer: x2-4y2 = 1

Let p be a moving point on hyperbola x24-y2 = 1, o be the origin of coordinates, and m be the midpoint of line OP, then the trajectory equation of point m is______ ．

Let m (x, y), then p (2x, 2Y) be substituted into hyperbolic equation to obtain x2-4y2 = 1, which is the trajectory equation of point m x2-4y2 = 1. Answer: x2-4y2 = 1

AB is the diameter of circle O, P is a point on the extension line of chord AC, AC = PC, the line Pb intersects circle O at point D, and CP = CD is obtained

It is proved that AB is ⊙ o diameter, ⊥ BC ⊥ AP, and AC = PC
The ABP is isosceles
There is ∠ a = ∠ P
∵ four points a, C, B and D are in common circle
∴∠A=∠D
∴∠P=∠D
∴CP=CD

In the circle O, the two strings AB are perpendicular to CD, the perpendicular foot is p, ab = CD = 8, the radius is 5, find Op

If the chord center distance OE, of between two strings AB and CD is given, then OE = of (the strings are equal)
So, oepf is a square, EP = OE
In the right triangle AOE, Ao = 5, AE = 4, so OE = 3
So, EP = 3. OP is the diagonal of the square oepf, so,
OP=3√2.

As shown in the figure, it is known that there is a point E in ⊙ o with radius 2, the chord AB passing through point E is perpendicular to CD, and OE = 1, then the value of AB2 + CD2 is equal to______ ．

Connect Ao, do, make om ⊥ CD at point m, make on ⊥ AB at point n, ∵ DC ⊥ AB, OM ⊥ DC, on ⊥ AB, ∵ quadrilateral omen is rectangular; ∵ om2 + me2 = oe2 (Pythagorean theorem), and ∵ me2 = on2 ≁ om2 + on2 = oe2; ∵ om2 = do2-dm2 = 4 - (DC2) 2; and ∵ on2 = oa2-an2 = 4 - (AB2) 2, ∵ om2 + on2

It is known that: the diameter of ⊙ o AB = 12cm, P is the midpoint of ob, through P, the chord CD intersects with AB to form an angle of 30 degrees, and the length of chord CD is calculated

Connect OC, make OE perpendicular to e through O, Op = 1 / 2ob = 1 / 2oC = 3 in triangle ope, OE = OP * sin30 = 3 / 2 in triangle OEC, according to Pythagorean theorem, CE = 3 (radical 15) / 2 can be calculated, so CD = 2ce = 3 (radical 15)

It is known that the diameter of circle O is ab = 12cm, P is the midpoint of ob, the chord CD is made through P, and ab intersects at an angle of 30 ° to find the length of chord CD

The vertical line of CD is made by O, the vertical foot is e, connecting OC
In the right triangle OEP, if OP = 3 and angle ope = 30 degrees, then OE = 1.5
In OEC of right triangle, OC = 6, using Pythagorean theorem, CE = √ (135 / 4), then
CD=2CE=√135cm

It is known that the diameter ab of the circle O is 12 cm, P is the midpoint of ob, and the chord CD is 30 degrees when passing through P?

Make the OE perpendicular to CD and connect to OC
In the right triangle Poe, the angle ope = 30 degrees, Op = 3, OE = 3 / 2
In the right triangle OCE, OC = 6, OE = 3 / 2, CE = 3 times root sign 15 / 2 can be obtained
According to the vertical diameter theorem, CD = 2ce = 3 times root sign 15

The diameter of circle O is ab = 16, P is the midpoint of ob, the chord CD passing through point P intersects AB at an angle of 30 degrees, and the length of chord CD is calculated. OE is obtained, and how to use Pythagorean theorem again

Connect OC and OD, make point O and make a vertical line to CD. If the vertical point is e, the angle OPD is 30 degrees. From this, OE = 2 can be calculated, OC is radius 8, CE can be calculated through the right triangle OCE, and then CD can be calculated

F1 and F2 are the two focal points of hyperbola, F1 is the focal point of parabola y ^ 2 = 4x, hyperbola passes a (- 2,0), B (2,0), find the trajectory equation of F2 Note the explanation of the value range of X Don't you know what to do?