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In the rectangular coordinate system xoy, the center is at the origin, and the focus is on the point on the ellipse C on the X axis In the rectangular coordinate system xoy, the center is at the origin, and the distance between the point (2 radical 2,1) on the ellipse C with the focus on the x-axis and the two focuses is 4 radical 3 (1) The standard equation of ellipse (2) The right focus F of the ellipse C makes a straight line L and the ellipse C intersect with two points a and B respectively, where the point a is below the X axis, and the vector AF = 3 times the vector FB. The equation of the circle passing through three points a, B and O is obtained
Let the standard equation of ellipse be x ^ 2 / 12 + y ^ 2 / b ^ 2 = 1. Let the point (2 roots, 2,1) be on the ellipse, then B ^ 2 = 3 can be solved. Therefore, the standard equation is x ^ 2 / 12 + y ^ 2 / 3 = 12. Let f (3,0) let the equation of line l be y = K (x-3), a (x1, Y1), B (X2, Y2) and eliminate y to (4K ^ 2 + 1)
Please describe the problem clearly. If you can't understand the problem, you can't answer it
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Given that the vertices B and C of △ ABC are on the ellipse x23 + y2 = 1, vertex A is a focus of the ellipse, and the other focus of the ellipse is on the edge of BC, then the perimeter of △ ABC is ()
A. 23B. 6C. 43D. 12
From the definition of ellipse: the sum of the distances from a point on the ellipse to two focal points is equal to the length of the major axis 2a, we can get that the perimeter of △ ABC is 4A = 43, so we choose C
Given that the vertices B and C of △ ABC are on the ellipse x23 + y2 = 1, vertex A is a focus of the ellipse, and the other focus of the ellipse is on the edge of BC, then the perimeter of △ ABC is ()
A. 23B. 6C. 43D. 12
From the definition of ellipse: the sum of the distances from a point on the ellipse to two focal points is equal to the length of the major axis 2a, we can get that the perimeter of △ ABC is 4A = 43, so we choose C
When sin (4 / 4 π - x) = 5 / 3, the value of sin2x is 0
sinπ/4cosx-cosπ/4sinx=3/5
(cosx-sinx)*√2/2=3/5
square
(1/2)(sin²x+cos²x-2sinxcosx)=9/25
1-sin2x=18/25
sin2x=7/25
seven-twenty-fifths
The image with positive scale function y = KX (k is Changshu, K is not equal to 0) passes through a point and a straight line of (1, K)
The image with positive scale function y = KX (k is Changshu, K is not equal to 0) passes through a straight line of points (0,0) and (1, K)
It has a common focus with the hyperbola x ＾ 2 / 16-y ＾ 2 / 4 = 1 and passes through the point (3 √, 2)
And passing through point (3 √ 2, 2),
Given a '& sup2; = 16, B' & sup2; = 4C '& sup2; = 16 + 4 = 20, then the hyperbola C & sup2; = 20b & sup2; = 20-a & sup2; so x & sup2; / A & sup2; - Y & sup2; / (20-a & sup2;) = 1 substitute the point into 18 / A & sup2; - 4 / (20-a & sup2;) = 1 de denominator 360-18a & sup2; - 4A & sup2; = 20A & sup2
The hyperbolic equation with common focus with hyperbola x ^ 2 / 16-y ^ 2 / 4 = 1 can be set as
X^2/k-Y^2/(25-k)=1
Substitution point (3 radical 2,2)
K = 15 or 32, but k > 0 25-k > 0, so k = 32 is omitted
k=15
X^2/15-Y^2/10=1
Given sin (45 degrees - x) = 3 / 5, the value of sin2x is?
sin45cosx-cos45sinx=3/5
√2/2(sinx-cox)=3/5
Square on both sides
1/2(sin²x+cos²x-2sinxcosx)=9/25
1-sin2x=18/25
sin2x=7/25
SiNx square + cosx square = 1 and the above simultaneous; sin2x = 2sinxcosx = 43 / 30 radical sign 2 of the knot
Given that the second power of the function y = (A-1) x to the power of a is a positive proportional function, we can find the value of A
A1 = 1 (incompatible, rounding off),
If y = (A-1) x ^ (A & sup2;). Is a positive proportional function, then
a-1≠0,a≠1.
a²=1,
A1 = 1 (incompatible, rounding off),
a2=-1.
The value of a is - 1
The standard equation for hyperbola: the length of the real axis is 10, the length of the imaginary axis is 8, and the focus is on the X axis
x^2/25-y^2/16=1
2a=10===>a=5
2b=8====>b=4
The standard equation of hyperbola: X & sup2; / 5 & sup2; - Y & sup2; / 4 & sup2; = 1
A = 10 / 2 = 5, B = 8 / 2 = 4,
So hyperbolic equation: x ^ 2 / 25-y ^ 2 / 16 = 1
a=5,b=4
Substituting into the hyperbolic basic equation x & sup2; / A & sup2; - Y & sup2; / B & sup2; = 1, we can get
x²/5²-y²/4²=1
Given sin (45-x) = 3 / 5, find sin2x
As above
Ask an expert to answer
The final result is 7 / 25, the process sin (45-x) = sin45cosx sinxcos45 = 3 / 5, the previous part is combined to get the root sign 2 / 2 (cosx SiNx) = 3 / 5, and the two sides are squared at the same time to get (cosx SiNx) ^ 2 = 18 / 25. Finally, the square is calculated to get 2sinxcosx = 7 / 25, sin2x = 2sinxcosx = 7 / 25
RELATED INFORMATIONS
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