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This is a minimisation problem, but it's slightly tricky to see what it is we're minimising. Seeing as it's a that's varying, we are going to have to differentiate with respect to a at some point. We're g...

First make left =0x²+y²-6x+4y+4=0Second put same terms together(x²-6x)+(y²+4y)+4=0Complete the Square (do a square (X+b)² that gives you you x^{2 ...}

Firstly, take a common denominator for the left hand-side of the equation which would be 12 and then carrying out the subtraction. After carrying out the subtraction you will be left with two fractions - ...

This is a simple simultaneous equationFirst we multiply the second equation by 3 to get 6X - 3Y = 30Then we add the first and second equation together to get 6X + X +3Y - 3Y = 30 + 19which we simply to 7X...

The most simple way to find the gradient of a quadratic curve at a point is to differentiate. Through differentiation a function for the gradient at each value of x can be found. 'y' must be isolated on o...