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aidmoon2x

Answered question

2021-11-19

How do I find the equation for a semicircle with a radius of 2 on the x axis?
Im

Geraldine Flores

Beginner2021-11-20Added 21 answers

Equation of a semi-circle at the origin:

y {(r^{2} - x^{2})}^{\frac{1}{2}}

To translate this to centre (a, b):

y = \sqrt{r^{2} - {(x - a)}^{2}} + b

The solution for your example SHOULD be:

y = \sqrt{4 - x^{2}} + 1.5

Except, its

Mollicchiuk

Beginner2021-11-21Added 13 answers

In general, if a circle has center

(a, b)

and radius r, then its equation is

{(x - a)}^{2} + {(y - b)}^{2} = r^{2}

The equation for that semicircle is therefore

x^{2} + {(y - 1.5)}^{2} = 4

with the restriction

x \geq 0

. If you wish, you can rewrite this as

x = \sqrt{4 - {(y - 1.5)}^{2}}

where

y \in [- \frac{12}{,} 3 \frac{1}{2}]

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