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