Equation of the Normal to the Parabola:
The equation for the normal to the parabola can be expressed as:
where
Simplifying, we have:

Center and Radius of the Circle:
The given second equation can be rewritten to find the center and radius of the circle:

Rewrite it as .
Thus, the center of the circle is and the radius .

Finding the Slope of the Normal:
To find the point on the parabola where the

normal meets, equate:

Solving for gives:

Determine Point on the Parabola:
Substituting back to find

Calculate the Shortest Distance:
The shortest distance from point to the center minus the radius is:

Thus, the shortest distance between the given curves is .

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