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Firstly notice that the coordinates of the points where the tangent to the curve is parallel to the x-axis are precisely the points where the rate of change of y with respect to x is not changing. That is...

logF=logG+logH−log(1/M)−2*logR Simplify RHS using law of logarithms, 

logF=log(GH)−log(1/M)−2logR             using law of addition
logF=log(GHM)−2logR                      ...

This question requires differentiating the equation to find where its gradient is equal to zero. Differentation is done via a simple equation -->  if y = xⁿ then dy/dx = nx^n-1

In order to answer this question, we must transform this equation for a circle into the general form of an equation of a circle; namely something like (x-a)²+(y-b)²=r². On...

To solve the equation in the form (ax + b)(x + c):

Method 1

1. Rewrite the x term as the sum of 2 different x terms. Start by multiplying the x^2 term and the final number term...