Question

1. state the equation of a circle with centre (0,0) that passes through the point (5,2). include a sketch.

Explanation:

Identify the standard equation of a circle

The standard equation of a circle centered at the origin \((0,0)\) is:

$$x^2 + y^2 = r^2$$

where \(r\) represents the radius of the circle.

Substitute the given point to find the radius squared

Using the Substitution Method from your mastered skills, we substitute the coordinates of the given point \((5,2)\) into the equation to solve for \(r^2\):

$$(5)^2 + (2)^2 = r^2$$

$$25 + 4 = r^2$$

$$r^2 = 29$$

Write the final equation of the circle

Substitute \(r^2 = 29\) back into the standard equation:

$$x^2 + y^2 = 29$$

This represents a circle centered at \((0,0)\) with a radius of \(\sqrt{29} \approx 5.39\).

Answer:

\(x^2 + y^2 = 29\)