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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…
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 …
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. parametric coordinates 2. parametric coordinates cartesian coordinates: curve is described by one equation and pointsare described by two numbers. 3. parametric coordinates…
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 …
locus problems locus problems (get rid of the p’s and q’s) locus problems (get rid of the p’s and q’s) we find the locus of a point. locus problems (get rid of the…
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. 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…
1. tangents & normals(ii) using cartesian 2. tangents & normals (ii) using cartesian (1) tangent 3. tangents & normals (ii) using cartesian (1) tangentyx 2 …
1. tangents & normals(i) using parametrics 2. tangents & normals (i) using parametrics (1) tangent 3. tangents & normals(i) using parametrics (1) tangentyx 2…
1. parametric coordinates 2. parametric coordinatescartesian coordinates: curve is described by one equation and points are described by two numbers. 3. parametric coordinatescartesian…
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…
locus problems locus problems eliminate the parameter (get rid of the p’s and q’s) locus problems we find the locus of a point. eliminate the parameter (get rid of the…
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. geometrical theorems about parabola 2. geometrical theorems about(1) focal chords parabola 3. geometrical theorems about (1) focal chordsparabolae.g. prove that the tangents…
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. 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. the parabola as a locus yx 2. the parabola as a locus ya point moves so that its distancefrom a fixed point (focus) isequal to its distance from a fixedline (directrix)x…
the parabola as a locus y x the parabola as a locus a point moves so that its distance from a fixed point (focus) is equal to its distance from a fixed line (directrix) y…