Provide an Analytic Proof for each of the following theorems. The perpendicular bisector of a chord of a circle contains the center.

Q: Sketch (hand-drawn or Maple-rendered) each the quadric surfaces listed below. Compute and include 3…

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Q: Which point lies on the graph of the unit circle? (1,  √3) (3/4,  √7/4) (1/3,  √2/3) ( √2,  √2)

A: A point lies on the unit circle if the sum of squares of x-axis and y-axis is 1 Mathematically,

Q: 2 Determine each of the following for the circle whose equation is x² The equation of the circle in…

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Q: Find the center and radius of the following circle. x²+2x+y² = 12y The center is . (Type an ordered…

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Q: Consider two circles in a plane. The first circle, C₁, has a radius of r₁ and is centered at point…

A: For the centers of the two circles C1 and C2 to coincide, the coordinates of their centers must be…

Q: A circle whose equation is x2 + y2 + 4x + 6y – 23 = 0 has its center at ______.

A: Given equation,

Q: Consider the circle C defined by the following equation. x²+y2-10x+2y+22=0 Complete the parts below.…

A: The given equation of the circle is x2 + y2 - 10x + 2y + 22 = 0. We can rewrite this in the standard…

Q: Find an equation of the circle in standard form with center at (1, 5) that is tangent to the x-axis.…

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Q: What is the radius of the following circle?    (x+12) 2 + (Y+6)2 =64

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Q: Given the points P(0,4) and Q(4,7): state the equation of a circle with center P and which has the…

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