DP Further Mathematics HL Questionbank

• Syllabus

2.6

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.