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Let y= f(x) be a curve C1 passing throug...

Let y= f(x) be a curve `C_1` passing through (2,2) and `(8,1/2)` and satisfying a differential equation `y(d^2y)/(dx^2)=2((dy)/(dx))^2` Curve `C_2` is the director circle of the circle `x^2+y^2=2` If the shortest distance between the curves `C_1` and `C_2` is `(sqrt(p)-q)` , then find the value of `(p^2-q)`

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