Why does my child think x² + y² = 25 has a radius of 25?
Your child mixes up the radius and its square, such as giving x² + y² = 25 a radius of 25 instead of 5.
Why children do it
The 25 is the only number in the equation, so it looks like the radius. But it's the radius squared: every point on the circle is a distance r from the centre, and Pythagoras gives x² + y² = r². So x² + y² = 25 has radius 5.
How to help at home
Ask them to find a point on the circle, like where it crosses the x-axis: how far is it from the centre?
The right way
What is the radius of the circle x² + y² = 25?
- 5 × 5 = 2525 is the radius squared.
- 5So the radius is 5.
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