# Worksheet: Equation of a Hyperbola

In this worksheet, we will practice analyzing and writing equations of hyperbolas.

**Q3: **

Suppose that we model an objectβs trajectory in the solar system by a hyperbolic path in the coordinate plane. The -axis is a line of symmetry of this hyperbola. The object enters in the direction of and leaves in the direction . The sun is positioned at the origin and the object passes within 1 AU (astronomical unit) of the sun at its closest. Using the asymptoteβs equations, find the equation of the objectβs path.

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**Q4: **

Suppose we model an asteroidβs trajectory by a hyperbolic path in the coordinate plane. The -axis is a line of symmetry of this hyperbola, and the object enters in the direction of and leaves in the direction . The sun is positioned at the origin, and the object passes within 1 AU (astronomical unit) of the sun at its closest such that the sun is one focus of the hyperbola. Give the equation of the objectβs path.

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**Q5: **

Suppose we model an asteroidβs trajectory by a hyperbolic path in the coordinate plane. The -axis is a line of symmetry of this hyperbola, and the object enters in the direction of and leaves in the direction . The sun is positioned at the origin, and the object passes within 1 AU (astronomical unit) of the sun at its closest such that the sun is one focus of the hyperbola. Give the equation of the objectβs path.

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**Q6: **

A hedge is to be constructed in the shape of a hyperbola near a fountain at the centre of a garden. The hedge will follow the asymptotes and , and its closest distance to the centre fountain is 6 yards. Find the equation of the hyperbola.

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**Q7: **

A hedge is to be constructed in the shape of a hyperbola near a fountain at the centre of a garden. The hedge will follow the asymptotes and , and its closest distance to the centre fountain is 5 yards. Find the equation of the hyperbola.

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**Q8: **

A hedge is to be constructed in the shape of a hyperbola near a fountain at the centre of a yard. The hedge will follow the asymptotes and , and its closest distance to the centre fountain is 10 yards. Find the equation of the hyperbola.

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**Q9: **

Write the equation of the rectangular hyperbola passing through with asymptotes meeting at .

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**Q10: **

Suppose that we model an objectβs trajectory in the solar system by a hyperbolic path in the coordinate plane, with its origin at the sun and its units in astronomical units (AU). The -axis is a line of symmetry of this hyperbola. The object enters in the direction of , leaves in the direction of , and passes within 1 AU of the sun at its closest point. Using the equations of the asymptotes, find the equation of the objectβs path.

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