Equation of a normal to a Circle from a given point

Given three integers a, b, c representing coefficients of the equation x² + y² + ax + by + c = 0 of a circle, the task is to find the equation of the normal to the circle from a given point (x₁, y₁).
Note: Normal is a line perpendicular to the tangent at the point of contact between the tangent and the curve.

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Examples:

Input: a = 4, b = 6, c = 5, x₁ = 12, y₁ = 14 
Output: y = 1.1x + 0.8

Input: a = 6, b = 12, c = 5, x₁ = 9, y₁ = 3 
Output: y = -0.5x + 7.5

Approach: Follow the steps below to solve the problem:

• The normal to a circle passes through the center of the circle.
• Therefore, find the coordinates of the center of the circle (g, f), where g = a/2 and f = b/2.
• Since the center of the circle and the point where the normal is drawn lie on the normal, calculate the slope of the normal (m) as m = (y₁ - f) / (x₁ - g). 
• Hence, the equation of the normal is y - y₁ = m * (x - x₁).

Below is the implementation of the above approach:

y = 1.1x + 0.8

Time Complexity: O(1)
Auxiliary Space: O(1)