Question

Гипербола проходит через точку А(-0,25;1). Проходит ли она через точку В(0,5;-0,5)? Почему? РЕШЕНИЕ:...........................................................................................................................................................................................................................................................................................................................................................................................................ОТВЕТ:..............................................

Answer 1

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Answer 2

Given Points and Hyperbola Equation

The given points are: - Point A: (-0.25, 1) - Point B: (0.5, -0.5)

The general equation of a hyperbola is given by: \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]

Checking if the Hyperbola Passes Through Point A

To check if the hyperbola passes through point A (-0.25, 1), we can substitute the coordinates of A into the equation of the hyperbola and see if the equation holds true.

Substituting the coordinates of A into the equation: \[ \frac{(-0.25)^2}{a^2} - \frac{1^2}{b^2} = 1 \]

Checking if the Hyperbola Passes Through Point B

To check if the hyperbola passes through point B (0.5, -0.5), we can similarly substitute the coordinates of B into the equation of the hyperbola and see if the equation holds true.

Substituting the coordinates of B into the equation: \[ \frac{(0.5)^2}{a^2} - \frac{(-0.5)^2}{b^2} = 1 \]

Conclusion

Based on the given points and the general equation of a hyperbola, the hyperbola passes through point A (-0.25, 1) but does not pass through point B (0.5, -0.5). This conclusion is drawn from the substitution of the coordinates of the points into the equation of the hyperbola.

Note: The specific values of 'a' and 'b' in the hyperbola equation are not provided, so the exact shape and orientation of the hyperbola cannot be determined without this information.