$\"\"$

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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.

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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 is $\"\"$ .

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$\"\"$

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

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Substitute $\"\"$ and $\"\"$ in the above formula.

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$\"\"$

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This is a pair of tangent lines.

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These tangent lines intersect the parabola, and the intersecting points can be determined by solving them.

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Substitute $\"\"$ in the curve $\"\"$ .

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$\"\"$

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

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

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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Therefore, the points at tangent lines intersect parabola are $\"\"$ and $\"\"$ .

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$\"\"$

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Graph:

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Graph the parabola with the tangent lines with intersecting points $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Intersecting points are $\"\"$ and $\"\"$ .

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Graph:

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$\"\"$ .