# 3 variables, 3 equations?

Calculus Level 5

Let $$C_1$$ and $$C_2$$ be defined as: $\large C_1:x^2+y^2+2\color{red}{g}x+2\color{blue}{f}y+\color{green}{c}=0$ $(g,f,c \text{ are real parameters})$

$\large C_2: y^2-4x+8=0$

If $$C_1$$ passes through the point $$(6,3)$$ and also cuts $$C_2$$ orthogonally at the point with ordinate $$-2$$ then $$C_1$$ can be written in the form mentioned above, then:

$\Large \color{red}{g}+\color{blue}{f}-\color{green}{c}=\ ?$

Inspiration

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