Porisma

A hint to get started

Ellipse and circle: three ways to obtain faithful sketches

Sketch the ellipses:

(a) (x−1)24+(y+2)29=1\dfrac{(x-1)^2}{4}+\dfrac{(y+2)^2}{9}=1,

(b) x2+y2−5x+y−52=0x^2+y^2-5x+y-\dfrac52=0,

and state the line(s) of symmetry.

CJC · Lecture · Example 4

For (a), read the centre and square roots of the denominators. For (b), complete the x- and y-squares independently before identifying the curve.

Read the worked solution