Respuesta :
Answer:
radius ≈ 17.0 units
Step-by-step explanation:
The radius is the distance from the centre of the circle to a point on it.
Calculate the radius r using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (7, 12)
r = [tex]\sqrt{(7+6)^2+(12-1)^2}[/tex]
= [tex]\sqrt{13^2+11^2}[/tex]
= [tex]\sqrt{169+121}[/tex]
= [tex]\sqrt{290}[/tex] ≈ 17.0 ( to the nearest tenth )
The required radius of the circle whose center is at the point (-6,1). If the point (7, 12) lies on the circle is 17.0
What is a circle?
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.
The radius of the circle r, for the center (h, k) and point on the circle (x, y) is given by the distance formula,
[tex]r = \sqrt{(x-h)^2 +(y-k)^2}[/tex]
Since the center is at the point (-6,1). If the point (7, 12) lies on the circle,
[tex]r = \sqrt{(7+6)^2 +(12-1)^2}\\r = \sqrt{(13)^2 +(11)^2}\\r = \sqrt{169+121}\\r =\sqrt{290}[/tex]
r = 17.03
r ≈ 17.0 (to the nearest tenth)
Thus, the required radius of the circle whose center is at the point (-6,1). If the point (7, 12) lies on the circle is 17.0
Learn more about circle here:
brainly.com/question/11833983
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