Further Maths: Conics Section 1: The conics and their graphs

Ms Rodgriues from Integral

Equation of parabola

y² = 4ax

The diagram below shows an example of a parabola in the case where is positive. So that y can be defined, cannot be negative. If a were negative, then x cannot be positive and so the parabola would be reflected in the ___

a
x
y-axis

PARABOLA Translation of a units in x direction

x - a

PARABOLA Translation of a units in y direction

y - a

PARABOLA Stretch of scale factor of a in the x direction

x / a

PARABOLA Stretch of scale factor of a in the y direction

y / a

PARABOLA Reflection in y = x

interchange x and y

Equation of ellipse

x² / a² + y² / b²= 1
This ellipse is centered on the origin and crosses the coordinate axes at (a,0) and (0, . b)

ELLIPSE you can replace x by _______ for a translation

x-k

ELLIPSE you can replace x by _______ for a stretch,

x / k

ELLIPSE you can replace y by ____ for a translation

y - k

ELLIPSE you can replace y by ______ for a stretch,

y / k

Equation of hyperbola

x² / a²- y² / b² = a

HYPERBOLA you can replace x by _______ for a stretch,

x - k

HYPERBOLA you can replace x by _______ for a stretch,

x / k

HYPERBOLA you can replace y by ____ for a translation

y / k