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The parabola is $\"\"$ .

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The both tangents to the parabola intersect on $\"\"$ axis are orthogonal .

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From the point of symmetry, the lines make angle of $\"\"$ with positive and negative $\"\"$ axis respectively.

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Therefore we can assume the points of tangency as $\"\"$ and $\"\"$ .

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Slope of the tangent line is derivative of the curve.

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$\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Find the slope at $\"\"$ .

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$\"\"$ .

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Find the slope at $\"\"$ .

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$\"\"$ .

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The two tangents are perpendicular to each other,so the product of their slopes is $\"\"$ .

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$\"\"$

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Substitute above value in the points $\"\"$ and $\"\"$ .

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

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$\"\"$

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Find the equation of tangent line $\"\"$ :

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Slope at $\"\"$ :

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$\"\"$ .

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

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

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$\"\"$

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$\"\"$

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Find the equation of tangent line $\"\"$ :

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Slope at $\"\"$ :

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$\"\"$ .

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

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

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$\"\"$

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Compare both tangent line equations with slope-intercept form $\"\"$ .

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$\"\"$ intercepts of these two lines are $\"\"$ and $\"\"$ .

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Thus the point of intersection on $\"\"$ axis is $\"\"$ .

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$\"\"$

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Graph:

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Graph of the parabola.

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Graph the tangent line equations.

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$\"\"$

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Observe the graphs.

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The tangent lines intersect on $\"\"$ axis at $\"\"$ .

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Graph of the parabola with tangents intersecting on $\"\"$ axis.

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$\"\"$ .