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The focus diretrix property for an ellipse is PS/PD=e. Now this is also the case for the other directrix and focus, so PS'/PD'=e. Now we can rearrange these equations to find a formula for PS +PS', PS +PS...

If you need to solve them, then you just plug your way through the algebra to get to the answer.

In this question (Q7) you need to find the value of a constant such that there is no solution to the...

First of all, we need to show that the statement is true for the base case n=1. For this case the expression becomes: 1+p≥1+p, which is clearly true as both sides are equal and hence solve the inequality....

1.Differentiating: f'(x)= 2cosh(x)+3sinh(x) At a stationary point, we know f'(x)=0. Therefore 2cosh(x)+3sinh(x)=0. (easy to forget that unlike nromal trig there is no change in sign) Rearranging gives tan...

Say arctan of x is equal to a value y. Now take the tangent of both sides; x now equals tan of y! Easy from here, differentiate both sides wrt x. Now 1 equals sec^2y dy/dx, and you can rearrange to find d...