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2.6

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Topic 2 - Geometry » 2.6

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Directly related questions

18M.2.hl.TZ0.5c: The centre of another ellipse is now given as the point (2, 1). The minor and major axes are of...
18M.2.hl.TZ0.5b.iv: Find the equations of the directrices.
18M.2.hl.TZ0.5b.iii: Find the coordinates of the foci.
18M.2.hl.TZ0.5b.ii: Hence find the eccentricity.
18M.2.hl.TZ0.5b.i: Determine which coordinate axis the major axis of the ellipse lies along.
18M.2.hl.TZ0.5a: Show that the area enclosed by the ellipse is \(\pi ab\).
17M.2.hl.TZ0.9b.iv: Hence find the coordinates of the foci of the hyperbola prior to rotation.
17M.2.hl.TZ0.9b.iii: Determine the equation of the rotated hyperbola in this case, giving your answer in the...
17M.2.hl.TZ0.9b.ii: Verify that the coefficient of \(XY\) in the equation is zero when \(\tan \alpha = \frac{1}{2}\).
15M.2.hl.TZ0.4f: Find the equations of the directrices of the ellipse.
15M.2.hl.TZ0.4e: Find the coordinates of the foci of the ellipse.
15M.2.hl.TZ0.4d: State the coordinates of the point where (PQ) touches the ellipse.
15M.2.hl.TZ0.4c: Hence show that (PQ) touches the ellipse.
15M.2.hl.TZ0.4b: Given that the tangent crosses the \(x\)-axis at P and the normal crosses the \(y\)-axis at Q,...
15M.2.hl.TZ0.4a: (i) Find the equation of the tangent to the ellipse at the point...
SPNone.1.hl.TZ0.5b: The distinct points \({\rm{P}}(a{p^2}, 2ap)\) and \(Q(a{q^2}, 2aq)\) , where \(p\), \(q \ne 0\) ,...
14M.1.hl.TZ0.6: The parabola \(P\) has equation \({y^2} = 4ax\). The distinct points...
14M.2.hl.TZ0.7: (a) (i) By first noting that \({\text{OP}} = x\sec \alpha \), show that...

Sub sections and their related questions

Conic sections.

SPNone.1.hl.TZ0.5b: The distinct points \({\rm{P}}(a{p^2}, 2ap)\) and \(Q(a{q^2}, 2aq)\) , where \(p\), \(q \ne 0\) ,...
14M.2.hl.TZ0.7: (a) (i) By first noting that \({\text{OP}} = x\sec \alpha \), show that...
18M.2.hl.TZ0.5a: Show that the area enclosed by the ellipse is \(\pi ab\).
18M.2.hl.TZ0.5b.i: Determine which coordinate axis the major axis of the ellipse lies along.
18M.2.hl.TZ0.5b.ii: Hence find the eccentricity.
18M.2.hl.TZ0.5b.iv: Find the equations of the directrices.
18M.2.hl.TZ0.5c: The centre of another ellipse is now given as the point (2, 1). The minor and major axes are of...
18M.2.hl.TZ0.5b.iii: Find the coordinates of the foci.

The parabola, ellipse and hyperbola, including rectangular hyperbola.

14M.1.hl.TZ0.6: The parabola \(P\) has equation \({y^2} = 4ax\). The distinct points...
15M.2.hl.TZ0.4c: Hence show that (PQ) touches the ellipse.
18M.2.hl.TZ0.5a: Show that the area enclosed by the ellipse is \(\pi ab\).
18M.2.hl.TZ0.5b.i: Determine which coordinate axis the major axis of the ellipse lies along.
18M.2.hl.TZ0.5b.ii: Hence find the eccentricity.
18M.2.hl.TZ0.5b.iv: Find the equations of the directrices.
18M.2.hl.TZ0.5c: The centre of another ellipse is now given as the point (2, 1). The minor and major axes are of...
18M.2.hl.TZ0.5b.iii: Find the coordinates of the foci.

Focus–directrix definitions.

15M.2.hl.TZ0.4e: Find the coordinates of the foci of the ellipse.
15M.2.hl.TZ0.4f: Find the equations of the directrices of the ellipse.
18M.2.hl.TZ0.5a: Show that the area enclosed by the ellipse is \(\pi ab\).
18M.2.hl.TZ0.5b.i: Determine which coordinate axis the major axis of the ellipse lies along.
18M.2.hl.TZ0.5b.ii: Hence find the eccentricity.
18M.2.hl.TZ0.5b.iv: Find the equations of the directrices.
18M.2.hl.TZ0.5c: The centre of another ellipse is now given as the point (2, 1). The minor and major axes are of...
18M.2.hl.TZ0.5b.iii: Find the coordinates of the foci.

Tangents and normals.

15M.2.hl.TZ0.4a: (i) Find the equation of the tangent to the ellipse at the point...
15M.2.hl.TZ0.4b: Given that the tangent crosses the \(x\)-axis at P and the normal crosses the \(y\)-axis at Q,...
15M.2.hl.TZ0.4c: Hence show that (PQ) touches the ellipse.
15M.2.hl.TZ0.4d: State the coordinates of the point where (PQ) touches the ellipse.
18M.2.hl.TZ0.5a: Show that the area enclosed by the ellipse is \(\pi ab\).
18M.2.hl.TZ0.5b.i: Determine which coordinate axis the major axis of the ellipse lies along.
18M.2.hl.TZ0.5b.ii: Hence find the eccentricity.
18M.2.hl.TZ0.5b.iv: Find the equations of the directrices.
18M.2.hl.TZ0.5c: The centre of another ellipse is now given as the point (2, 1). The minor and major axes are of...
18M.2.hl.TZ0.5b.iii: Find the coordinates of the foci.