Problem of the Week

Problem 32

An ellipse with a centre at the origin (p,q) can be written in the form:

$\frac{(x-p)^2}{a^2} + \frac{(y-q)^2}{b^2} = 1$

Where $a+p$ is the largest $x$ -coordinate on the circumference of the ellipse and $b+q$ is the largest $y$ -coordinate on the circumference of the ellipse.

a) What is the equation of the ellipse centred at the origin which passes through the points (-2.4, 0.8) (0,1) and (0,-1)?

b) What is the equation(s) of the ellipse centred at (4,1) whose distance between its largest $x$ and $y$ -coordinate on the circumference is 13 and a and b are integers?

c) What is the equation of the largest ellipse that is contained within the parallelogram of (-8,-1), (8,-1), (-4, 1) and (12, 1)?

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Problem of the Week

Problem 32

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