Question Video: Finding the Equation of a Circle given Its Altitude and a Relation between the Altitude and Its Radius Mathematics

The radius of the area in which a rocket may land is three times its current altitude. If a rocket’s altitude is 333 feet, write the equation that describes its landing circle, assuming its center is at the origin.

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Video Transcript

The radius of the area in which a rocket may land is three times its current altitude. If a rocket’s altitude is 333 feet, write the equation that describes its landing circle, assuming its center is at the origin.

As we are told the radius is three times its current altitude, we can calculate the radius of the circle by multiplying three by 333 β€” the current altitude. This is equal to 999 feet. The equation of any circle is given by π‘₯ minus π‘Ž all squared plus 𝑦 minus 𝑏 all squared is equal to π‘Ÿ squared, where the center of the circle has coordinates π‘Ž, 𝑏 and the radius of the circle is equal to π‘Ÿ.

As we’re told the center of the circle is at the origin, we can say that the center has coordinates zero, zero. Substituting these values into the equation of a circle gives us π‘₯ minus zero all squared plus 𝑦 minus zero all squared is equal to 999 squared. 999 squared is 998001. π‘₯ minus zero is π‘₯ and 𝑦 minus zero is 𝑦.

Therefore, the equation of the circle is π‘₯ squared plus 𝑦 squared is equal to 998001. We can therefore say that this is the equation that describes the landing circle of the rocket.

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