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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?
Equation of the circle: (x-3)^2 +( y+13)^2 = 169
Is a circle symmetric with respect to x-axis on a graph?
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.
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?
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
What does rotate and rotation mean?
rotate is moving in a circle around an axis or center. Rotation is the action of rotating around an axis or center.
How are the discriminant and the graph of a quadratic equation related?
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
How do you find the zeros in an equation by looking on a graph?
They are all the points where the graph crosses (or touches) the x-axis.
What is the equation of the circle passing through the origin and having center at y - axis?
x2 + (y - b)2 = b2 or, equivalently, x2 + y2 - 2by = 0
How can you tell if a parabola moves up or down in an equation?
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.
The ellipse graphed below has its center at -2 2 its horizontal axis is of length 6 and its vertical axis is of length 10 What is its equation?
23
How you find the solution of a quadratic equation by graphing its quadratic equation?
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.
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.
Does the center of circle turn at the double speed as the outside if radius is double?
The centre of the circle does not turn at all: the axis of rotation goes through it.
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