It is known that the equation of the ellipse is x ^ 2 / 3 + y ^ 2 / 4 = 1 and the branch line is L = 1 / 4x + M. try to determine the value range of M. there are two different points on the ellipse that are symmetrical about the line In two ways

It is known that the equation of the ellipse is x ^ 2 / 3 + y ^ 2 / 4 = 1 and the branch line is L = 1 / 4x + M. try to determine the value range of M. there are two different points on the ellipse that are symmetrical about the line In two ways

Let two points a (x1, Y1), B (X2, Y2) on the known ellipse be symmetric with respect to the straight line, let the equation of the straight line where AB is located be y = - 4x + N, substitute it into the conic equation, get the quadratic equation of one variable with respect to x, write out the discriminant, X1 + X2, and then express Yi + Y2 with X1 + X2, write out the midpoint coordinate formula, bring in the symmetry axis, get a relation, and then substitute this relation into the discriminant

Ellipse C and ellipse (x − 3) 29 + (Y − 2) 24 = 1 are symmetric with respect to the straight line x + y = 0. The equation of ellipse C is ()
A. (x+2)24+(y+3)29＝1B. (x−2)29+(y−3)24＝1C. (x+2)29+(y+3)24＝1D. (x−2)24+(y−3)29＝1

According to the meaning of the question, we can see that the ellipse C is symmetrical about the straight line x + y = 0, the major axis and minor axis remain unchanged, and the center of the main ellipse is OK. ∵ the center of the ellipse (x − 3) 29 + (Y − 2) 24 = 1 is (3,2) the point of symmetry about the straight line x + y = 0 is (- 2, - 3), so the equation of the ellipse C is (x + 2) 24 + (y + 3) 29 = 1, so we choose a