"A circle has a center at (1, 2)..." solved and explained

Leonel Dunlap

Answered question

2022-02-12

A circle has a center at

(1, 2)

and passes through

(4, 7)

. What is the length of an arc covering

\frac{π}{4}

radians on the circle?

Katrina Patton

Beginner2022-02-13Added 11 answers

Step 1
Let us denote by S the Circle, by r radius, and pt.

C (1, 2) =

Centre of S, and a pt

P (4, 7)

on S
Then, dist

C P = r

, and, using Dist. Formula, we get,

r^{2} = C P^{2} = {(4 - 1)}^{2} + {(7 - 2)}^{2}

= 9 + 25 = 34

giving

r = \sqrt{34}

The arc subtends angle

θ = \frac{p I}{4}

at the centre, so that,
Length of Arc

= r \times θ = \sqrt{34} \times \frac{π}{4} \tilde{=} 5.84 \times \frac{3.41}{4} = 4.58

unit

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