EasyMathematicsHigh School (11–12)Coordinate Geometry › Circles and Conic SectionsNumerical

The rim of a circular metal dish is drawn on a plan as 2x² + 2y² - 8x + 12y - 10 = 0, with lengths…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

The rim of a circular metal dish is drawn on a plan as $2x^2 + 2y^2 - 8x + 12y - 10 = 0$ , with lengths in decimetres. A worker needs the centre and the radius to set a compass. Find the coordinates of the centre and the radius.

Need a reminder? The key ideaShow

The circle with centre $(h, k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$ . Opening the brackets gives $x^2 + y^2 + 2gx + 2fy + c = 0$ with centre $(-g, -f)$ and radius $\sqrt{g^2 + f^2 - c}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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