DP Further Mathematics HL Questionbank

• Syllabus

2.5

Sub sections and their related questions

Finding equations of loci.

• 07M.1.hl.TZ0.1a: Find the equation of the locus of P.
• 12M.2.hl.TZ0.1B.a: When \(k = 1\) , show that the locus of P is a straight line.
• 12M.2.hl.TZ0.1B.b: When \(k \ne 1\) , the locus of P is a circle.   (i)     Find, in terms of \(k\) , the...
• 14M.1.hl.TZ0.6: The parabola \(P\) has equation \({y^2} = 4ax\). The distinct points...
• 15M.1.hl.TZ0.10a: Find the coordinates of \({\text{A}}\) in terms of \(r\) and \(\theta \).
• 15M.1.hl.TZ0.16: A circle \({x^2} + {y^2} + dx + ey + c = 0\) and a straight line \(lx + my + n = 0\) intersect....
• 18M.1.hl.TZ0.15: Given that the tangents at the points P and Q on the parabola \({y^2} = 4ax\) are perpendicular,...

Coordinate geometry of the circle.

• 07M.1.hl.TZ0.1b: Show that this equation represents a circle and state its radius and the coordinates of its centre.
• 14M.1.hl.TZ0.14: (a)     The function \(g\) is defined by \(g(x,{\text{ }}y) = {x^2} + {y^2} + dx + ey + f\) and...
• 15M.1.hl.TZ0.16: A circle \({x^2} + {y^2} + dx + ey + c = 0\) and a straight line \(lx + my + n = 0\) intersect....
• 18M.1.hl.TZ0.15: Given that the tangents at the points P and Q on the parabola \({y^2} = 4ax\) are perpendicular,...

Tangents to a circle.

• 18M.1.hl.TZ0.15: Given that the tangents at the points P and Q on the parabola \({y^2} = 4ax\) are perpendicular,...