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If given two parametric equations for a curve, how would you work out an equation for the gradient?

Parametric equations will have both the x and the y coordinates expressed in terms of another paramater, usually t. Gradients of curves are expressed in the form of an equation of dy/

Answered by Mollie W. • Maths tutor

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Show that Sec2A - Tan2A = (CosA-SinA)/(CosA+SinA)

Sec2A - Tan2A Definition of Sec and Tan = 1/Cos2A - Sin2A/Cos2A Combining Fractions = (1 - Sin2A) / (Cos2A) Apply Double Angle Formula = (1 - 2SinACosA) / (Cos²A - Sin²A) Make use of...

Answered by James C. • Maths tutor

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Solve: x^2-7x+6=0

Factorise the equation and then equate each set of brackets to 0 to obtain both possible solutions.

By factorising: (x-6)(x-1)=0

Therefore: x=6 or x=1

Answered by Phoebe G. • Maths tutor

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Line AB has equation 4x+5y+2=0. If the point P=(p, p+5) lies on AB, find P . The point A has coordinates (1, 2). The point C(5, k) is such that AC is perpendicular to AB. Find the value of k.

i) Well, if point P lies in AB, then the value of its x and y coordinates have to fulfill the condition imposed by equation AB. Therefore, substituting the x value p for x and the y value p+5 for y:

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Answered by Javier L. • Maths tutor

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(A-Level) Find the coordinate of the stationary point of the curve y = 2x + 27/x^2

Since we are looking for a stationary this means the derivative will be equal to 0, so we will have to differentiate the equation. When we differentiate ( y = 2x + 27/x^2 ) we get ( dy/dx = 2 - 54/x^3 ). ...

Answered by Vlad B. • Maths tutor

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