Math  /  Geometry

Question9 L'équation du deramethe de ('hyperbole 4x25y2=104 x^{2}-5 y^{2}=-10 qui passe par le milien de la carde purtrei pan la anse 2x+y+3=02 x+y+3=0 as:
1. 5y8x=05 y-8 x=0 \quad 2. 8yx=035y+2x=08 y-\sqrt{x}=0 \quad 3 \quad 5 y+2 x=0 \quad 4. 8y+2x=08 y+2 x=0 55y2x=05 \quad 5 y-2 x=0

Studdy Solution
Determine the equation of the diameter of the hyperbola that passes through this midpoint:
The equation of the diameter of a hyperbola is given by the line passing through the midpoint of the chord and parallel to the conjugate axis.
Since the hyperbola is in the form x2a2y2b2=1\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, the conjugate axis is vertical.
Thus, the diameter is a vertical line passing through the midpoint MM.
The correct equation of the diameter is:
5y2x=0 \boxed{5y - 2x = 0}

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