FP1.4 - Coordinate systems

Cartesian equations for the parabola Students should be familiar with the equations: and rectangular hyperbola. c y2 = 4ax or x = at2, y = 2at and xy = c2 or x = ct, y =. t.

Use fp1.4.1 - cartesian equations for the parabola to connect the rule to the data and decision in the question.

This matters because fp1.4.1 - cartesian equations for the parabola determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp1.4.1 - cartesian equations for the parabola to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.

Idea of parametric equation for The idea of (at2, 2at) as a general point on the parabola is parabola and rectangular hyperbola. all that is required.

Use fp1.4.2 - parametric equations for conics to connect the rule to the data and decision in the question.

This matters because fp1.4.2 - parametric equations for conics determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp1.4.2 - parametric equations for conics to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.

The focus-directrix property of the Concept of focus and directrix and parabola as locus of parabola. points equidistant from focus and directrix.

Use fp1.4.3 - focus-directrix property of the parabola to connect the rule to the data and decision in the question.

This matters because fp1.4.3 - focus-directrix property of the parabola determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp1.4.3 - focus-directrix property of the parabola to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP1.4.3 - Focus-directrix property of the parabola is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Tangents and normals to these 1 1 c2 Differentiation of y = 2a2x2, y =. curves. x Parametric differentiation is not required.

Use fp1.4.4 - tangents and normals to conics to connect the rule to the data and decision in the question.

This matters because fp1.4.4 - tangents and normals to conics determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply fp1.4.4 - tangents and normals to conics to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: FP1.4.4 - Tangents and normals to conics is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.