A circle that is centered at the origin contains the point (0,4). How can you prove or disprove that the point (2, 6 ) also lies on the circle? Does the point (2, 6 ) lie on the circle? A) Substitute the radius and the point (0,4) into x2 + y2 = r2 and simplify. The point (2, 6 ) lies on the circle. B) Substitute the points (0,4) and (2, 6 ) into the distance formula.The point (2, 6 ) lies on the circle. C) Substitute the radius and the point (2, 6 ) into x2 + y2 = 1 and simplify. The point (2, 6 ) does not lie on the circle. D) Substitute the radius and the point (2, 6 ) into x2 + y2 = r2 and simplify. The point (2, 6 ) does not lie on the circle.
Answers
Given : A circle that is centered at the origin contains the point (0,4).
To find : point (2, 6) lies on circle or not
Solution:
Equation of Circle
(x - h)² + ( y - k)² = r²
(h , k ) is center & r is radius
circle that is centered at the origin
=> (h , k) = ( 0 , 0)
=> x² + y² = r²
circle contains the point (0,4).
=> 0² + 4² = r²
=> r = 4
Equation of circle become
x² + y ² = 4²
point (2, 6 )
=> LHS = 2² + 6² = 40
RHS = 16
40 ≠ 16
LHS ≠ RHS
Hence 2 , 6 Does not lie on circle
Substitute the radius and the point (2, 6 ) into x2 + y2 = r2 and simplify. The point (2, 6 ) does not lie on the circle.
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