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What is the equation of the tangent line that meets the circle x2 -4x plus y2 -6y equals 4 at the point 6 4?
Circle equation: x^2 -4x +y^2 -6y = 4
Completing the squares: (x-2)^2 +(y-3)^2 = 17
Point of contact: (6, 4)
Center of circle: (2, 3)
Slope of radius: 1/4
Slope of tangent line: -4
Tangent equation: y-4 = -4(x-6) => y = -4x+28
Tangent line equation in its general form: 4x+y-28 = 0
What else can I help you with?
What is the Radius tangent theorem?
The tangent of a circle always meets the radius of a circle at right angles.
What is the point of contact when the tangent line y -3x -5 equals 0 meets the circle x2 plus y2 -2x plus 4y -5 equals 0?
It works out that the tangent line of y -3x -5 = 0 makes contact with the circle of x^2 + y^2 -2x +4y -5 = 0 at (-2, -1)
What is the distance from the centre of a circle to a point on the x axis that forms a tangent line when it meets the circle of x2 plus y2 -2x -6y plus 5 equals 0 at the point 3 and 4?
Point of contact: (3, 4) Circle equation: x^2 +y^2 -2x -6y+5 = 0 Completing the squares: (x-1)^2 +(y-3)^2 -1 -9 +5 = 0 So: (x-1)^2 +(y-3) = 5 Centre of circle: (1, 3) Slope of radius: (3-4)/(1-3) = 1/2 Slope of tangent: -2 Equation of tangent line: y-4 = -2(x-3) => 2x+y = 10 Tangent line meets the x axis at: (5, 0) Using formula distance from (1, 3) to (5, 0) = 5 units
What is the length of tangent line from -2 3 to the point of contact with the circle x2 plus y2 plus 6x plus 10y minus 2 equals 0?
Equation of circle: x^2 +y^2 +6x +10y -2 = 0 Completing the squares: (x+3)^2 +(y+5)^2 = 36 Radius of circle: 6 Center of circle: (-3, -5) Distance from (-2, 3) to (-3, -5) is sq rt of 65 which is hypotenuse of a right triangle Using Pythagoras' theorem: square root of 65^2 -6^2 = 29 Therefore length of tangent line is the square root of 29 Note that the tangent line of any circle always meets its radius at right angles which is 90 degrees.
What is a Chords in circles?
A chord is a straight line drawn through a circle which divides the circle into two parts. The line can be drawn anywhere in the circle EXCEPT the center where it becomes the diameter.
What is the radius equation inside the circle x squared plus y squared -8x plus 4y equals 30 that meets the tangent line y equals x plus 4 on the Cartesian plane showing work?
Circle equation: x^2 +y^2 -8x +4y = 30 Tangent line equation: y = x+4 Centre of circle: (4, -2) Slope of radius: -1 Radius equation: y--2 = -1(x-4) => y = -x+2 Note that this proves that tangent of a circle is always at right angles to its radius
What is the Radius tangent theorem?
The tangent of a circle always meets the radius of a circle at right angles.
What happens where a radius meets the tangent?
The radius and the tangent are perpendicular at the point on the circle where they meet.
What is an Angle whose side is tangent to a circle called?
There is no specific name for such an angle.
What is the tangent equation line of the circle x2 plus 10x plus y2 -2y -39 equals 0 at the point of contact 3 2 on the Cartesian plane?
Equation of circle: x^2 +10x +y^2 -2y -39 = 0 Completing the squares: (x+5)^2 +(y-1)^2 = 65 Center of circle: (-5, 1) Slope of radius: 1/8 Slope of tangent line: -8 Point of contact: (3, 2) Equation of tangent line: y-2 = -8(x-3) => y = -8x+26 Note that the tangent line meets the radius of the circle at right angles.
The point at which a tangent line meets a circle is called the point of tangency?
true
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
Does a trigonometry tangent relate to a circle's tangent?
A circle's tangent is exactly the same as a triangle's tangent. If you look at a circle, you can make the radius the hypotenuse. Then make a vertical line from the point, and a horizontal line from the center. If you look, you have a triangle made inside the circle. This is why angles can be measured in radians, a unit that is derived from the circumference of a circle.-------------------------------------------------------------------------------------------By doing a little calculus, we find that the slope of the equation of a circle-the slope of the tangent line-is given by the tangent of an angle.AnswerEverything written above is correct, but doesn't have anything to do with tangents (in the circle sense of the word). Suppose you're given an angle theta. Draw a circle together with two radii, one horizontal and the other at an angle theta from the first one. (So far, this is the same as above.) Now draw the tangent to the circle at X, the point where the non-horizontal radius meets the circumference. Let Y be the point where this tangent meets the horizontal line through the centre. Then, assuming the radius is 1, tan(theta) is the distance XY, which is the length of part of the tangent.
What is the distance to the center of the circle x2 plus y2 -2x -6y plus 5 equals 0 from the x axis at the same point when the tangent line meets the x axis from the point 3 4?
Equation of circle: x^2 +y^2 -2x -6y +5 = 0 Completing the squares: (x-1)^2 +(y-3)^2 = 5 Center of circle: (1, 3) Tangent line from (3, 4) meets the x axis at: (5, 0) Distance from (5, 0) to (1, 3) = 5 using the distance formula
Difference between secant lines and tangent lines?
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
What is the term for a line that meets a circle or arc at only one point on it's exterior so it will not go through the circle?
a tangent to the circle
What is the point of contact when the tangent line y -3x -5 equals 0 meets the circle x2 plus y2 -2x plus 4y -5 equals 0?
It works out that the tangent line of y -3x -5 = 0 makes contact with the circle of x^2 + y^2 -2x +4y -5 = 0 at (-2, -1)
