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/Tag: Locus
11 09, 2016

Circles & Lines

Circles & Lines Perpendicular distance = radius, then tangent Perpendicular distance < radius, line intersects circle at 2 points Perpendicular distance > radius, line does not intersect with the circle   x2 + y2 = r2    Circle centre (0, 0) radius = r units (x - a)2 + [...]

12 08, 2015

12 08, 2015

y squared – not origin

y squared - not origin (y - k)2 = 4a(x - h) Vertex (h, k) Focal length = a worked examples A parabola has equation 2y² = 4x + 8 a. Express this equation in the form (y - y1)²=4a(x - x1). b. Draw a neat sketch of the parabola indicating [...]

12 08, 2015

x squared – not origin

x squared - not origin (x - h)2 = 4a(y - k) Vertex (h, k) Focal length = a worked examples Express y = x2 + 2x – 5 in the form (x – h)2 = 4a(y – k), given a, h and k are constants. x2 + [...]

12 08, 2015

Focal Length – Not Origin

Focal Length - Not Origin worked examples  A parabola had equation y = x² - 4x + 6, find its focal length. x² - 4x = y - 6  Equation of parabola is: (x - h)2 = 4a(y - k) where a is the focal length and (h, [...]

12 08, 2015

Equation of a Parabola

By |2016-11-03T14:30:30+10:00August 12th, 2015|Tags: , , |0 Comments

Equation of a Parabola General Equation of a Parabola: ax2 + bx + c = 0 x2 = 4ay is the equation of a parabola with the vertex at the origin, and the y-axis (x = 0) as the axis of symmetry. a is the focal length of the parabola. That [...]

12 08, 2015

Tangents To Circle

By |2016-10-21T13:17:30+10:00August 12th, 2015|Tags: , , , |0 Comments

Tangents To Circle If perpendicular distance from centre < r - no intersection If perpendicular distance from centre = r - tangemt If perpendicular distance from centre > r - two points of intersection worked examples   tr_ap_97, q4a Show the line 4x + 3y + 10 = 0 is a [...]

12 08, 2015