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Sagot :
Given:
The point (7, 4) lies on a circle centered at the origin.
To find:
The equation of the circle and the radius of the circle.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The point (7, 4) lies on a circle centered at the origin. So, the distance between the points (7,4) and (0,0) is equal to the radius of the circle.
[tex]r=\sqrt{(0-7)^2+(0-4)^2}[/tex]
[tex]r=\sqrt{(-7)^2+(-4)^2}[/tex]
[tex]r=\sqrt{49+16}[/tex]
[tex]r=\sqrt{65}[/tex]
The standard form of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(i)
Where, (h,k) is the center of the circle and r is the radius of the circle.
Putting h=0, k=0 and [tex]r=\sqrt{65}[/tex] in (ii), we get
[tex](x-0)^2+(y-0)^2=(\sqrt{65})^2[/tex]
[tex]x^2+y^2=65[/tex]
Therefore, the equation of the circle is [tex]x^2+y^2=65[/tex] and its radius is [tex]r=\sqrt{65}[/tex].
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