Find the x-coordinate, in terms of a and m, where y is maximal.

01 / Standard#Your turn

x,y>0,\quad0<m<1,\quad y^2-2mxy+x^2=a^2

Official paper · jm01-2021 · II.3(c) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the equality condition from part (b).

Hint 2

Take the positive square root for y.

Worked solution

Positive y and the squared bound give its maximum.
$y_{\max}=\sqrt{a^2/(1-m^2)}=|a|/\sqrt{1-m^2}$
Multiply by m using x=my.
$x_0=\frac{m|a|}{\sqrt{1-m^2}}$

x=m|a|/√(1−m²).

Checks and common pitfalls: The sign of a is unspecified, so √(a²)=|a|.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Positive y and the squared bound give its maximum.
$y_{\max}=\sqrt{a^2/(1-m^2)}=|a|/\sqrt{1-m^2}$
Multiply by m using x=my.
$x_0=\frac{m|a|}{\sqrt{1-m^2}}$

Think first. Reveal a hint when the class is ready.

2021 JM01