A circle centred at M(4,4) is tangent to y=2x. Find its equation.

01 / Standard#Your turn

M=(4,4),\quad L_1:2x-y=0

Official paper · jm01-2021 · II.2(a) · PDF 4

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

The radius is the perpendicular centre-to-line distance.

Hint 2

Square that distance in the circle equation.

Worked solution

Use the point-line distance formula.
$r=\frac{|2(4)-4|}{\sqrt{2^2+(-1)^2}}=4/\sqrt5$
Insert the centre and radius.
$(x-4)^2+(y-4)^2=16/5\iff5x^2+5y^2-40x-40y+144=0$

(x−4)²+(y−4)²=16/5.

Checks and common pitfalls: The oblique distance from the origin to M is not the circle radius.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Use the point-line distance formula.
$r=\frac{|2(4)-4|}{\sqrt{2^2+(-1)^2}}=4/\sqrt5$
Insert the centre and radius.
$(x-4)^2+(y-4)^2=16/5\iff5x^2+5y^2-40x-40y+144=0$

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

2021 JM01