$\"\"$

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

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The point passing through the parabola is $\"\"$ .

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Tangent line equation passing through $\"\"$ is $\"\"$ .

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The point $\"\"$ passes through parabola.

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Substitute $\"\"$ in the parabola equation.

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$\"\"$

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$\"\"$

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Tangent line equation is $\"\"$ .

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The line equation is in the form of slope intercept form of line equation $\"\"$ .

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Compare tangent line equation with slope intercept form.

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Here slope $\"\"$ .

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Slope of the tangent line is the derivative of the function at $\"\"$ .

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The parabola equation is $\"\"$ .

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

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$\"\"$

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Slope at point $\"\"$ :

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Substitute $\"\"$ in the above equation.

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$\"\"$

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

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$\"\"$ .

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$\"\"$

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The point of tangency passes through the curve.

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Substitute $\"\"$ in the parabola equation.

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$\"\"$

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Substitute $\"\"$ in the above equation.

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$\"\"$ .

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Solve equation $\"\"$ and $\"\"$ .

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Subtract equation $\"\"$ from equation $\"\"$ .

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$\"\"$

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

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$\"\"$

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

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$\"\"$

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The parabola equation is $\"\"$ .

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$\"\"$

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The parabola equation is $\"\"$ .