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Firstly, we know that dy/dx is the gradient of the tangent to a curve. If we know the gradient of the tangent, and the point on the curve where the tangent touches it, we can work out the equation of the ...

i) multiply out: 3x3+kx2-3x-21x2-7kx+21 simplify: 3x3+(k-21)x2+(-7k-3)x+21 the coefficient of x2 is 0 and therefore k-21=0 k=21.
ii)from i) the c...

The general equation of a circle is (x-a)^2 + (y-b)^2 = r^2 where the centre is (a,b) and radius r.
Therefore the equation of this circle is (x-3)^2 +(y-4)^2 = 4^2 ...or 16
Sometimes its easie...