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In the plane rectangular coordinate system of the figure, the parabola y = - 4 / 3x 2 + 8 / 3x + 4 intersects the X axis at two points a and B As shown in the plane rectangular coordinate system of the figure, the parabola y = - 4 / 3x? + 8 / 3x + 4 intersects the X axis at two points a and B (point B is on the right side of point a), the y-axis intersects at point C, with OC and ob as the two sides to make rectangular obdc, and CD intersects the parabola at G (1) Find the length of OC and ob; (2) Let OE = m, PM = h, find the function relation between H and m, and find the maximum value of PM; (3) If PC is connected, is there such a point P in the parabola above CD, so that the triangle with P, C and F as the vertices is similar to △ BEM? If so, directly calculate the value of m at this time and directly judge the shape of △ PCM. If not, please explain the reason I know the answer, but the third problem is to the third power. How to solve it!
Question 3:
When m = 23 / 16, △ PFC is similar to △ BEM, and △ PCM is a triangle with right angle C
When m = 1, △ CFP is similar to △ BEM, where △ PCM is an isosceles triangle and PM is the base
As shown in the figure, in the plane rectangular coordinate system, the parabola y = - x2 + 3x + 5 intersects point a and B with X axis (a is on the left side), and intersects with y axis at point C. the vertex of parabola is point m, which is symmetrical As shown in the figure, in the plane rectangular coordinate system, the parabola y = - x2 + 3x + 4 and X axis intersect at points a and B (a is on the left), and y-axis intersects at point C. the vertex of the parabola is point m, the axis of symmetry and line BC intersect at point n, and point P is a moving point on segment BC (not coincident with B and C) Question: find a point D on the symmetry axis of parabola to make the value of | dc-db | maximum, and find the coordinates of point D; The solution connects AC and extends the symmetry axis of the intersecting parabola to d, Replace the coordinates of point a (- 1,0), C (0,4) into y = KX + B, b＝4 −k+b＝0 The solution is: B = 4, k = 4, The analytic formula of straight line AC is obtained: y = 4x + 4, By substituting x = 1.5 into y = 4x + 4, the, y=10, The coordinates of point d (1.5,10) Why is the absolute dc-db value the largest?
From the drawing, LDB DCL = AC
If D, a, C are not on the same line, then there will be △ DAC
According to the triangle trilateral relationship, it is not difficult to obtain LDB DCL < AC (the difference between any two sides of a triangle is less than the third side)
Therefore, LDB DCL is the largest when D, a and C are collinear
As shown in the figure, the image of the first order function y = - 4x-4 intersects with the x-axis and the y-axis respectively at two points a and C. the image of the parabola y = 4 / 3x? + BX + C passes through two points a and C, and intersects with the x-axis at point B ① Find parabola in function expression (I calculate y = 4 / 3x? - 8 / 3x-4) ② Let the parabola be d at the vertex, and find the area of quadrilateral ABCD (I find it is 12) ③ Make a straight line Mn parallel to the x-axis and intersect AC and BC at points m, N. ask if there is a point P on the x-axis so that △ PMN is an isosceles right triangle. Find out the coordinates of all P points that meet the conditions. If not, please explain the reasons Make it clear
Answer: (1) the first order function y = - 4x-4 and the intersection point a (- 1,0), point C (0, - 4), into the parabolic equation y = 4x ^ 2 / 3 + BX + C, we get: 4 / 3-B + C = 0C = - 4, B = - 8 / 3, so the parabola equation is y = 4x ^ 2 / 3-8x / 3-4 (2) parabola y = 4x ^ 2 / 3-8x / 3-4 = (4 / 3) * (x-1) ^ 2-16 / 3, vertex D (
The image with parabola y = 1 / 3 (X-2) 2 + 3 can be represented by parabola y = 1 / 3x The coordinates of its vertices are () and its axis of symmetry is ()
The image of parabola y = 1 / 3 (X-2) 2 + 3 can be obtained by translating (3) units upward and (2) units to the right of the parabola y = 1 / 3x? 2. Its vertex coordinates are (2,3) and its axis of symmetry is (x = 2)
As shown in the figure, it is known that AB is the diameter of ⊙ o, and point C is The middle point of AE is the chord CD ⊥ AB through C, and AE is intersected with F. it is proved that AF = CF
Proof: connect AC,
∵ chord CD ⊥ AB, AB is the diameter of ⊙ o,
Qi
AC=
AD，
∵ point C is
The midpoint of AE,
Qi
AC=
CE，
Qi
AD=
CE，
∴∠ACD=∠CAE，
∴AF=CF．
In the plane rectangular coordinate system xoy, the intersection points of the curve y = x? - 4x + 3 and the two coordinate axes are all on the circle C (1) Find the equation of circle C; (2) Whether there is a real number a, so that the circle C and the straight line X-Y + a = 0 intersect at two points a and B, and satisfy ∠ AOB = 90 °. If there is, find the value of a; if not, please explain the reason
1) Let the equation of circle C be (X-2) ^ + (y-b) ^ = R ^, then 1 + B ^ = R ^, 4 + (3-B) ^ = R ^, then 6b-12 = 0, B = 2, R ^ = 5, the equation of circle C is (X-2) ^ + (Y-2) ^ = 5
In the plane rectangular coordinate system xoy, the intersection point of the curve y = x? - 6x + 1 and the coordinate axis
y=x²-6x+1
y=(3x+1)(-2x+1)
Intersection with X axis (- 1 / 3,0) (1 / 2,0)
Focus with y axis (0,1)
It is known that the circle C: x2 + y2-6x-4y + 8 = 0. Taking the intersection point of circle C and coordinate axis as a focus and vertex of hyperbola respectively, the standard equation suitable for the above condition hyperbola is______ .
Circle C: x2 + y2-6x-4y + 8 = 0,
Let y = 0 to obtain x2-6x + 8 = 0,
The intersection points of circle C and coordinate axis are (2,0), (4,0), respectively,
Then a = 2, C = 4, B2 = 12,
So the standard equation for hyperbola is
X2
Four
−
Y2
Twelve
＝1．
So the answer is:
X2
Four
−
Y2
Twelve
＝1．
In the rectangular coordinate system xoy, it passes through the hyperbola x2 a2−y2 If M is the midpoint of FP, then | om | - | MT | is equal to () A. b-a B. a-b C. a+b Two D. a+b
Let the right focus be F2, | PF | - | PF2 | = 2A,
Connect PF2, OM is the median line, so | PF2 | = 2 | OM|
|PF|=2|MF|=2（|TF|+|MT|）
|Of | = C, | ot | = a, so | ft | = B
∴2（b+|MT|）-2|OM|=2a
∴b+|MT|-|OM|=a
∴|OM|-|MT|=b-a．
Therefore, a
In the plane rectangular coordinate system xoy, the intersection points of curve y = x square - 4x + 3 and two coordinate axes are all on circle C, (1) find the equation of circle C, (2) whether there is real number A. make circle C and straight line X-Y + a = 0 intersect at two points, and satisfy the angle AOB = 90 degrees. If there is, find the value of a, if not, explain the reason
In the attachment is my answer, because it can not be made into JPG format, it can only be made into PDF
RELATED INFORMATIONS
- 1. In the plane rectangular coordinate system xoy, the intersection points of the curve y = x ^ 2-4x + 3 and the two coordinate axes are all on the circle C 1) Find the equation of circle C 2) Is there a real number a such that the circle C and the straight line X-Y + a = 0 intersect at two points a and B, and the angle AOB is 90 degrees
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