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Center of circle: (2, 5)

Point of contact with the x axis: (2, 0)

Distance from (2, 5) to (2, 0) equals 5 which is the radius of the circle

Equation of the circle: (x-2)^2 +(y-5)^2 = 25

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6y ago

It is (x - 2)2 + (y - 5)2 = 25.

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Q: What is the equation of the circle that touches the x axis when its center is at 2 5?
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What are the tangent equations to the circle x2 plus y2 -6x plus 4y plus 5 equals 0 at the points where they meet the x axis?

Equation of circle: x^2 +y^2 -6x +4y +5 = 0 Completing the squares (x -3)^2 +(y +2)^2 = 8 Centre of circle: (3, -2) Radius of circle: square root of 8 Points of contact are at: (1, 0) and (5, 0) where the radii touches the x axis Slope of 1st tangent line: 1 Slope of 2nd tangent line: -1 Equation of 1st tangent: y -0 = 1(x -1) => y = x -1 Equation of 2nd tangent: y -0 = -1(x -5) => y = -x +5


Why does a circle have infinite lines of symmetry?

Because the distance from one point at the circumference through the center to another point at the circumference is always the same, at an infinite set of coordinates along the circle (anywhere, relative to the size of the circle, and always providing an axis which perfectly dissects the circle).


What is tangent to the x axis?

Well, since a tangent line touches a line in one spot, the Y axis could be considered tangent to the X axis.


Are axes and lines of symmetry the same thing?

No, although they can be lines of symmetry, they are not the same things. If a circle were to have its center at the point (1,1), the circle would have an infinite number of lines of symmetry, but none of them would be the x or y axis.


Find the differential equation of all circles tangent to y-axis?

Let the circle with centre (a, b) be tangent to the y-axis. Then, the radius of the circle must be b. Therefore the equation of the circle is (x - a)2 + (y - b)2 = b2 or x2 - 2ax + a2 + y2 - 2by = 0 Then 2x - 2a + 2ydy/dx - 2bdy/dx = 0 ie x - a + ydy/dx - bdy/dx (y - b)dy/dx = a - x so dy/dx = (a - x)/(y - b) or -(x - a)/(y - b)

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The center of a circle is located at c(3-13). The x-axis is tangent to the circle at (30). Find the equation of the circle?

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Is a circle symmetric with respect to x-axis on a graph?

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What is the tangent line equation of the circle x2 plus y2 -8x -16y -209 equals 0 when it touches the circle at 21 8 on the Cartesian plane?

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What are the tangent equations of the circle x2 plus y2 -6x plus 4x plus 5 equals 0 when it cuts through the x axis?

Equation of circle: x^2 +y^2 -6x+4y+5 = 0 Completing the squares: (x-3)^2 +(y+2)^2 = 8 Radius of circle: square root of 8 Center of circle: (3, 2) The tangent lines touches the circle on the x axis at: (1, 0) and (5, 0) 1st tangent equation: y = x-1 2nd tangent equation: y = -x+5 Note that the tangent line of a circle meets its radius at right angles


What is the tangent equation that touches the circle x2 -y2 -8x -16y -209 equals 0 at the point of 21 and 8 on the Cartesian plane?

Point of contact: (21, 8) Equation of circle: x^2 -y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) and its radius is 17 Slope of radius: 0 Slope of tangent: 0 Tangent equation of the circle: x = 21 meaning that the tangent line is parallel to the y axis and that the radius is parallel to the x axis.


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