How to find the center of a circle given the three points (-3,5); (3,3); (11,19)?

povzpetifkzf

povzpetifkzf

Answered question

2023-02-22

How to find the center of a circle given the three points (-3,5); (3,3); (11,19)?

Answer & Explanation

GreerceViemkpy2

GreerceViemkpy2

Beginner2023-02-23Added 5 answers

Step 1: Given that:
The given function is
y = A s i n 2 x

Given range, x = 0 → x = π
Step 2: Calculation of the average value of the given function:
Average value of a function ( < y > ) = ∫ y d x ∫ d x
Now, for a given range, the average value will be,

< y >= ∫ 0 π A sin 2 ⁡ x d x ∫ 0 π d x
< y >= A ∫ O π 1 − cos ⁡ 2 x 2 d x ∫ 0 π x O d x
< y >= A ( ∫ O π 1 2 d x − 1 2 ∫ O π cos ⁡ 2 x d x ) [ x O π ]
Now, ∫ cos ⁡ n x d x = 1 n sin ⁡ n x
< y >= A ( 1 2 ( x O π ) − 1 2 ( 1 2 cos ⁡ 2 x O π ) ) [ x O π ]
< y >= A [ 1 2 ( π − O ) − 1 4 ( cos ⁡ 2 π − cos ⁡ O ) π − O ]
Since, cos ⁡ 2 π = cos ⁡ O = 1 < y >= A [ π 2 π ]
< y >= A 2

Hence, the given function's average value in the given range will be
A 2
.




resymeguv48h

resymeguv48h

Beginner2023-02-24Added 7 answers

Equal distances separate the points from the center (a, b). Using the distance squares as an equation,
( a + 3 ) 2 + ( b - 5 ) 2 = ( a - 3 ) 2 + ( b - 3 ) 2 = ( a - 11 ) 2 + ( b - 19 ) 2 ,
From the first two,
3 a - b = 4 , and from first and the third,
a + b = 16 .
solving, (a, b) = (3, 13)...

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