[tex] \huge \qquad \sf \underline{\boxed{ {☘ \sf Sσlutiσn}}}[/tex]
The distance between the centre and any point satisfying the circle is its radius ~
Hence, the distance between the points is equal to length of radius.
[tex]\qquad \sf \dashrightarrow \: r = \sqrt{(4 - 1) {}^{2} + (9 - 5) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: r = \sqrt{(3) {}^{2} + (4) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: r = \sqrt{9 + 16} [/tex]
[tex]\qquad \sf \dashrightarrow \: r = \sqrt{25} [/tex]
[tex]\qquad \sf \dashrightarrow \: r = 5[/tex]
As we know, equation of a circle is :
[tex] \qquad \sf(x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
where,
Hence, equation of our required clrcle is :
[tex] \qquad \sf(x -1 ) {}^{2} + (y - 5) {}^{2} = {5}^{2} [/tex]
The radius of the circle that has center (1,5) and contains the point (4,9) is 5 units
The center of the circle is given as:
Center (a,b) = (1,5)
The point on the circle is given as:
Point (x,y) = (4,9)
The radius is calculated using the following distance equation
[tex]r = \sqrt{(x - a)^2 + (y - b)^2}[/tex]
So, we have:
[tex]r = \sqrt{(4 - 1)^2 + (9 - 5)^2}[/tex]
Evaluate the exponents
[tex]r = \sqrt{25}[/tex]
Take the square root of 5
r = 5
Hence, the radius of the circle is 5 units
Read more about circle equations at:
https://brainly.com/question/1559324
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