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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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Equation of the circle: (x-3)^2 +( y+13)^2 = 169

Any point on the graph can be the center of a circle. If the center is on the x-axis, then the circle is symmetric with respect to the x-axis.

Equation of circle: x^2 +y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Radius of circle: 17 Center of circle: (4, 8) Point of contact: (21, 8) Slope of radius: 0 Slope of tangent line: 0 Equation of tangent line: x = 21 which means it touches the circle at (21, 0) which is a straight vertical line parallel to the y axis

rotate is moving in a circle around an axis or center. Rotation is the action of rotating around an axis or center.

If the discriminant = 0 then the graph touches the x axis at one point If the discriminant > 0 then the graph touches the x axis at two ponits If the discriminant < 0 then the graph does not meet the x axis

They are all the points where the graph crosses (or touches) the x-axis.

x2 + (y - b)2 = b2 or, equivalently, x2 + y2 - 2by = 0

Look at the discriminant, B2 - 4AC, in the quadratic equation. As it goes from negative to positive, the parabola moves in the direction of its small end towards the X-axis. At zero, it touches the X-axis.

23

When you graph the quadratic equation, you have three possibilities... 1. The graph touches x-axis once. Then that quadratic equation only has one solution and you find it by finding the x-intercept. 2. The graph touches x-axis twice. Then that quadratic equation has two solutions and you also find it by finding the x-intercept 3. The graph doesn't touch the x-axis at all. Then that quadratic equation has no solutions. If you really want to find the solutions, you'll have to go to imaginary solutions, where the solutions include negative square roots.

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.

The centre of the circle does not turn at all: the axis of rotation goes through it.

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