$\"\"$

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The equation of parabola is $\"\"$ and the point is $\"\"$ .

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Slope of the tangent is derivative of the curve at given point.

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$\"\"$

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

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$\"\"$

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Slope of the tangent at $\"\"$ is

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$\"\"$

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Slope of the tangent line is $\"\"$ .

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Tangent line is perpendicular to the normal line.

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If the two lines are perpendicular then their slopes will be $\"\"$

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

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$\"\"$ .

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Slope of the normal line is $\"\"$ . $\"\"$

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Point-slope form of line equation : $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the point - slope form.

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$\"\"$

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Find the intersection points of normal line and parabola by solving them.

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$\"\"$

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substitute $\"\"$ in curve.

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$\"\"$

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Substitute $\"\"$ values in $\"\"$ .

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

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First point is $\"\"$ .

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

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The second point is $\"\"$ . $\"\"$

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Graph:

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Graph the parabola with normal line intersecting second time at $\"\"$ .

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$\"\"$

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$\"\"$ \ \

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The required point is $\"\"$ .

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Graph:

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$\"\"$