Step 1:

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$\"\"$ -coordinate is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ -coordinate is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The distance from the point $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Step 2:

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The rate of change in distance with respect to $\"\"$ is $\"\"$ .

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$\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The rate of change at $\"\"$ .

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Find $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Step 3:

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The rate of change in distance at $\"\"$ is $\"\"$

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Substitute $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The rate of change in distance at $\"\"$ is $\"\"$ .

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Solution:

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The rate of change in distance at $\"\"$ is $\"\"$ .