$\"\"$

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Observe the graph :

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Focus $\"\"$ is $\"\"$ .

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Equation of tangent line is $\"\"$ .

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Since the point on the graph lie on $\"\"$ -axis, $\"\"$ .

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

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$\"\"$

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The point is at $\"\"$ and $\"\"$ is at $\"\"$ .

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Find lengths of the legs of the isosceles triangle.

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$\"\"$

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$\"\"$

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The lengths of the legs of the isosceles triangle are $\"\"$ .

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$\"\"$

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Since the lenghth of the isosceles traingle are $\"\"$ , the distance from $\"\"$ to the point of tangency $\"\"$ is $\"\"$ .

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Find the tangent line distance.

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

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$\"\"$

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Substitute $\"\"$ in above equation.

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$\"\"$

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$\"\"$

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

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At $\"\"$ , the value of $\"\"$ is $\"\"$ .

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Find the the value of $\"\"$ at $\"\"$ .

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

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$\"\"$

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$\"\"$

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At $\"\"$ , the value of $\"\"$ is $\"\"$ .

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The point of tangency line is located at $\"\"$ .

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$\"\"$

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The equation of parabola is $\"\"$ .

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Focus $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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

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The parabola lie on above $\"\"$ - axis, so $\"\"$ is positive.

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Thus, the value of $\"\"$ is $\"\"$ .

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$\"\"$

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Find the equation of a parabola.

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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The parabola equation is $\"\"$ . $\"\"$

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The parabola equation is $\"\"$ .