GCSE(H)

Pythagoras Theorem states that the sum of the square of the two shorter sides is equal to the square of the hypotenuse:

`a^2 + b^2 = c^2`

where *a* and *b* are the two shorter sides, and *c* is the long side.

Replace the *a* and *b* with *x* and *y* coordinates. Setting `x^2 + y^2 = r^2`, and keeping *r* constant, describes a circle of radius *r* with a centre at the origin.

1. A function is defined as `x^2 + y^2 = 64`. Construct the graph.

Answer:

The radius of the circle is `sqrt64`. The centre of the circle is at 0,0, with radius 8.

2. A function is defined as `x^2 + y^2 = 50`. Is the coordinate (4, 3) within the circle?

Answer: Yes

Work out the value of `4^2 + 3^2` = 25. This is less than 50, so the coordinates is within the circle.

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