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Hyperbola and inverse proportion function X2 / a2-y2 / B2 = 1 and xy = k What's the connection
Let the hyperbolic standard equation be x ^ 2 / A ^ 2 - y ^ 2 / b ^ 2 = 1 (a > 0, b > 0)
The standard form of the inverse proportional function is xy = C (C ≠ 0)
But the inverse scale function is really a hyperbolic function obtained by rotation
Because the axis of symmetry of xy = C is y = x, y = - x, and the axis of symmetry of x ^ 2 / A ^ 2 - y ^ 2 / b ^ 2 = 1 is x, y
So it should be rotated 45 degrees
Let the rotation angle be a (a ≠ 0, clockwise)
(a is the inclination angle of the hyperbolic asymptote)
There are
X = xcosa + ysina
Y = - xsina + ycosa
Let a = π / 4
be
X^2 - Y^2 = (xcos(π/4) + ysin(π/4))^2 -(xsin(π/4) - ycos(π/4))^2
= (√2/2 x + √2/2 y)^2 -(√2/2 x - √2/2 y)^2
= 4 (√2/2 x) (√2/2 y)
= 2xy.
And xy = C
therefore
X^2/(2c) - Y^2/(2c) = 1 (c>0)
Y^2/(-2c) - X^2/(-2c) = 1 (c
Any circle has innumerable axes of symmetry______ ．
If a circle is folded in half along the straight line with any diameter, the two parts after folding can completely coincide, so there are innumerable axes of symmetry in a circle
Leave a diameter in a circle
Such as the title
There are two
They are the straight line passing through the center of the circle along the diameter direction and the straight line passing through the center of the circle perpendicular to the diameter
A circle has numerous axes of symmetry, and each axis passes through its center
Judgment, pro,
Judgment:
A circle has numerous axes of symmetry, and each axis passes through its center
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