It is known that the ellipse takes the symmetry axis as the coordinate axis, and the major axis is three times of the minor axis, and passes through the point (3,0)

① If the focus is on the X axis, let the equation of the ellipse be x2a2 + y2b2 = 1 (a > b > 0), according to the meaning of the problem, a = 3, B = 1, the equation of the ellipse is X29 + y2 = 1; ② if the focus is on the Y axis, let the equation of the ellipse be y2a2 + x2b2 = 1 (a > b > 0), according to the meaning of the problem, a = 9, B = 3, the equation of the ellipse is y281 + X29 = 1. The standard equation of the ellipse is X29 + y2 = 1 or y281 + X29 = 1

The length of the major axis is twice that of the minor axis, and the standard equation of the ellipse passing through point (2,1) is?

It is easy to know that 2A = 2 (2b) = = = = > A = 2B. (1) let the elliptic equation be (X & sup2 / 4B & sup2;) + (Y & sup2 / B & sup2;) = 1. (2) let the elliptic equation be (X & sup2 / 8) + (Y & sup2; / 2) = 1

The equation of a straight line passing through point (1, - 1) and tangent to the square of circle x square + (y + 2) = 2 is
It's better to explain how each step comes and show up

Let the linear equation be y + 1 = K (x-1), that is, kx-y-k-1 = 0
The center of the circle is (0, - 2) and the radius is root 2
Tangency
| 2-k-1 | / root (1 + K ^ 2) = root 2
The result is: K ^ 2 + 2K + 1 = 0
The solution is k = - 1
The tangent equation is: - X-Y = 0, that is, x + y = 0

It is known that the ellipse takes the symmetry axis as the coordinate axis, and the major axis is three times of the minor axis, and passes through the point (3,0)