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Ellipse C rectangular coordinate equation 4 / x square + 3 / y square = 1, determine the value range of M, straight line L; y = 4x + m, there are two different points on ellipse C symmetrical about straight line L Please know the answer to this question friends, can give detailed and quick reply, thank you
Let there be two points a (x1, Y1), B (X2, Y2)
Then the midpoint m (x0, Y0) of AB is in the ellipse and on the straight line y = 4x + M
AB perpendicular to the line y = 4x + M
List known relationships:
3x1 ^ 2 + 4Y1 ^ 2 = 12... 1 (a on ellipse)
3x2 ^ 2 + 4y2 ^ 2 = 12... 2 (B on ellipse)
2x0 = X1 + X2.3 (M is the midpoint of AB)
2y0 = Y1 + y2.4 (ditto)
Y0 = 4x0 + m.5 (m on the line y = 4x + m)
(y1-y2) / (x1-x2) = - 1 / 4... 6 (AB perpendicular to the line y = 4x + m)
3x0^2+4y0^2
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