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locus locus the collection of all points whose location is determined by some stated law. locus locus the collection of all points whose location is determined by some stated

1. locus 2. locuslocusthe collection of all points whose location is determined by somestated law. 3. locus locusthe collection of all points whose location is determined

locus problems locus problems (get rid of the ps and qs) locus problems (get rid of the ps and qs) we find the locus of a point. locus problems (get rid of the

locus problems locus problems eliminate the parameter (get rid of the ps and qs) locus problems we find the locus of a point. eliminate the parameter (get rid of the

1. the parabola as a locusy x 2. the parabola as a locusya point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed line (directrix)x

concavity concavity the second deriviative measures the change in slope with respect to x, this is known as concavity concavity up concave is curve the,0 if

1. parametric coordinates 2. parametric coordinates cartesian coordinates: curve is described by one equation and pointsare described by two numbers. 3. parametric coordinates

1. geometrical theorems aboutparabola 2. geometrical theorems about (1) focal chordsparabola 3. geometrical theorems about(1) focal chords parabola e.g. prove that the tangents

1. tangents & normals(ii) using cartesian 2. tangents & normals (ii) using cartesian (1) tangent 3. tangents & normals (ii) using cartesian (1) tangentyx 2

the second derivative the second derivative 2 2 2 2 ,,, dx yd xf dx d xfy the second derivative 2 2 2 2 ,,, dx

1. tangents & normals(i) using parametrics 2. tangents & normals (i) using parametrics (1) tangent 3. tangents & normals(i) using parametrics (1) tangentyx 2

1. maxima & minima problems 2. maxima & minimaproblems when solving word problems we need to; 3. maxima & minima problems when solving word problems we need to;

geometrical applications of differentiation the first derivative geometrical applications of differentiation the first derivative dx dy xf dx d xfy

1. parametric coordinates 2. parametric coordinatescartesian coordinates: curve is described by one equation and points are described by two numbers. 3. parametric coordinatescartesian

1. geometrical theorems about parabola 2. geometrical theorems about(1) focal chords parabola 3. geometrical theorems about (1) focal chordsparabolae.g. prove that the tangents

chord of contact chord of contact y x 2 4x ay chord of contact y x 2 4x ay we know the coordinates of an external point (t) chord of contact y x 2 4x ay 0

1. chords of a parabola 2. chords of a parabola (1) chord 3. chords of a parabola (1) chord y x 2 4ay x 4. chords of a parabola (1) chord y x 2

1. chord of contact 2. chord of contact y x 2 4ay x 3. chord of contact y x 2 4ay we know the coordinates of an external point (t) x 4. chord of contacty x 2

1. locus 2. locus locus the collection of all points whose location is determined by some stated law. 3. locuslocus the collection of all points whose location is determined

locus problems locus problems eliminate the parameter (get rid of the ps and qs) locus problems we find the locus of a point. eliminate the parameter (get rid of the