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(a)

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The point $\"\"$ is in first quadrant.

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Required points having $\"\"$ - coordinate as $\"\"$ and distance from $\"\"$ is $\"\"$ .

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Plot the circle center at $\"\"$ and radius of the circle is $\"\"$ .

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Since $\"\"$ -coordinate is $\"\"$ , Plot the point $\"\"$ .

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Connect the plotted points.

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Find the coordinates left and right of $\"\"$ lies on the circle.

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Pythagorean theorem:

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$\"\"$ $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Case 1:

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$\"\"$

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$\"\"$ .

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Case 2:

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$\"\"$

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$\"\"$ .

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$\"\"$ , $\"\"$ .

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The points have $\"\"$ -coordinate as $\"\"$ , whose distance $\"\"$ from $\"\"$ are $\"\"$ , $\"\"$ . Graph:

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The points have $\"\"$ -coordinate as $\"\"$ , whose distance $\"\"$ from $\"\"$ are $\"\"$ , $\"\"$ .

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(b)

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The point $\"\"$ is in first quadrant.

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Required points having $\"\"$ - coordinate as $\"\"$ and distance from $\"\"$ is $\"\"$ .

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Calculate the distance between two points by using distance formula,

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$\"\"$ .

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$\"\"$ , $\"\"$ and $\"\"$ .

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Substitute $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ , $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ in above formula.

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$\"\"$

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$\"\"$

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$\"\"$

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Squaring on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply zero product property.

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$\"\"$ and $\"\"$

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

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The points have $\"\"$ -coordinate as $\"\"$ , whose distance $\"\"$ from $\"\"$ are $\"\"$ , $\"\"$ .

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The points are $\"\"$ and $\"\"$ .