UPDATE: Thanks for guiding Chang-Er Miss Loi safely to the moon. She shares some heavenly mooncakes with the rabbit last night! Yummy!
While the ritz and glitz of last Friday begins to fade into memory, the Mid-Autumn Festival is here again!
A time to commemorate a legend, a time for Hello Kitty lanterns with endlessly-repeating subliminal tunes, and a time when Miss Loi receives some delicious mooncakes from students and friends to gorge herself silly.
And so feeling rather hungry after a long day of lessons, she decided to drive to a nearby park to devour savour those mooncakes under the moonlight, totally forgetting what happened the last time she did some … umm … moonlighting.
In popped a snow-white morsel into her mouth, as she closed her eyes and surrendered to that heavenly flavour creeping up her taste buds, with the full moon looming large and bright above.
Unfortunately, no one told an alcohol-intolerant Miss Loi that the mooncakes were laced with liquor, and she soon found herself feeling tipsy coupled with a floating sensation …
.
.
.
When she opened her eyes, she discovered to her horror that the moon was now very much larger than before, and appeared to be drawing her towards it like a tractor beam!
As her long hair trailed in the cool night breeze, she had an even greater shock when she looked back and realized that she had left her handbag (yes the same big un-glam one she carried upstage last Friday) on the park bench that was rapidly receding into the distance – causing her to struggle like a mad woman in a bid to retrieve her bag.
Alarmed by what she had just witnessed, a rabbit stopped whatever she was pounding on the moon and yelled out to Miss Loi:
OMG you’re the Chang-Er with the WORST buoyancy control I’ve ever seen!
Stop struggling!!! You’re veering off-course! Land on the moon ASAP or you’ll be heading for outer space!
Invoking her powers of Coordinate Geometry, Miss Loi saw that:
The circular moon has a centre that lies on the line:
2x + y – 1 = 0
and its circumference passing through the points A(-2, 0) and B(5, 1).
To help Miss Loi land safely on the moon, find the coordinates of its centre and its radius, and hence deduce the equation of the moon.
With the introduction of Circles into the New A-Maths Syllabus this year, students are now required to know the equation of a circle, which may be expressed in standard form:
Equation of a Circle in Standard Form
(x – a)2 + (y – b)2 = r2
where C is the centre of the circle at coordinates (a, b) and r is its radius.
N.B. There’s also a General Form (to be discussed at another time)
Also, being a part of the Coordinate Geometry chapter, questions on Circles are often intertwined with bits and pieces from a variety of basic Coordinate Geometry topics like Midpoint of a Line Segment, Equations of Straight Lines, Perpendicular Lines etc. as well as the Geometric Properties of Circles which you’ve learnt in your Sec 3 E-Maths Mensuration.
Hence, good foundation is needed to bring Miss Loi to the moon!
