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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)
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 circles have their centers on the y-axis?
The circles that have their centers on the y-axis are those that have the equation x^2 + (y-k)^2 = r^2, where k is the y-coordinate of the center of the circle and r is the radius of the circle. In this case, the x-coordinate of the center is 0 since it lies on the y-axis.
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.
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.
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.
How many times does the graph of the function below touch or cross the x-axis 4x2-7x 40?
Without knowing the plus or minus value of 40 it's difficult to say but in general:- If the discriminant of a quadratic equation = 0 then it touches the x axis at 1 point If the discriminant is greater than zero then it touches the x axis at 2 points If the discriminant is less than zero then it does not touch the x axis
