Get the answer to "The point (1,3) lies on the circle that..."

High School
Geometry
High school geometry
Circles

opatovaL

Answered question

2021-03-08

The point (1, $\sqrt{3}$ ) lies on the circle that is centered at the origin and contains the point (0,2). Prove or disprove that.

Answer & Explanation

Mitchel Aguirre

Skilled2021-03-09Added 94 answers

The standard equation of a circle with center (h,k) and radius r is given by:
${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$
Using $(h, k) = (0, 0)$ and $(x, y) = (0, 2)$ , we solve for r2:
$(0 - 0) 2 + (2 - 0) 2 = r 2$
$4 = r 2$
So, the equation of the circle is:
$x^{2} + y^{2} = 4$
The point (1, $\sqrt{3}$ ) lies on the circle if it satisfies the equation so we check:
$1^{2} + {(\sqrt 3)}^{2} = ? 4$
$1 + 3 = ? 4$
$4 = 4$
Since it satisfies the equation, then $(1, \sqrt 3)$ lies on the circle.

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