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What are the lengths of the tangent lines from the point 8 2 when they touch the circle x2 plus y2 -4x -8y -5 equals 0 on the Cartesian plane showing work?
Tangent lines stem from the point: (8,2)
Equation of circle: x^2 +y^2 -4x -8y -5 = 0
Completing the squares: (x-2)^2 +(y-4)^2 -4 -16 -5 = 0
So: (x-2)^2 +(y-4)^2 = 25 which is the radius squared
Centre of circle: (2, 4)
Distance from (2, 4) to (8, 2) = 40 which is the distance squared
Lengths of tangents using Pythagoras: 40-25 = 15 => square root of 15
Note that the distance from (2, 4) to (8, 2) is actually the hypotenuse of a right angle triangle.
What else can I help you with?
What are the lengths of the tangent lines from the point 7 -2 to the circle x2 plus y2 -10y -24 equals 0 on the Cartesian plane?
Equation of circle: x^2 +y^2 -10y -24 = 0 Completing the square: x^2+(y-5)^2 = 49 Center of circle: (0, 5) Radius of circle: 7 Distance from (7, -2) to (0, 5) = sq rt of 98 and is the hypotenuse of a right triangle Using Pythagoras: theorem: distance^2 minus radius^2 = 49 Therefore lengths of tangent lines are square root of 49 = 7 units
Tangent of a circle is what?
A tangent of a circle is a straight line that touches the circle at only one point.
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
Where is the tangent secant angle on a circle?
The tangent secant angle is the angle between the tangent to a circle and the secant, when the latter is extended.
How do you find the tangent of a circle?
a tangent is a line that touches the circle at only ONE point
What is the tangent equation that touches the circle of x squared plus y squared -8x -y plus 5 equals 0 at the point of 1 2 on the Cartesian plane showing work?
Equation of circle: x^2 +y^2 -8x -y +5 = 0Completing the squares: (x-4)^2 +(y-0.5)^2 = 11.25Centre of circle: (4, 0.5)Slope of radius: -1/2Slope of tangent: 2Equation of tangent: y-2 = 2(x-1) => y = 2xNote that the above proves the tangent of a circle is always at right angles to its radius
What are the lengths of the tangent lines from the point 7 -2 to the circle x2 plus y2 -10y -24 equals 0 on the Cartesian plane?
Equation of circle: x^2 +y^2 -10y -24 = 0 Completing the square: x^2+(y-5)^2 = 49 Center of circle: (0, 5) Radius of circle: 7 Distance from (7, -2) to (0, 5) = sq rt of 98 and is the hypotenuse of a right triangle Using Pythagoras: theorem: distance^2 minus radius^2 = 49 Therefore lengths of tangent lines are square root of 49 = 7 units
Tangent of a circle is what?
A tangent of a circle is a straight line that touches the circle at only one point.
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 equation of a circle whose diameter endpoints are at 2 -3 and 8 7 on the Cartesian plane and what are the tangent equations touching its endpoints showing work?
Endpoints: (2, -3) and (8, 7)Centre of circle: (5, 2)Radius of circle is the square root of 34Equation of the circle: (x-5)^2 +(y-2)^2 = 34Slope of radius: 5/3Slope of tangents: -3/51st tangent equation: y--3 = -3/5(-2) => 5y = -3x-92nd tangent equation: y-7 = -3/5(x-8) => 5y = -3x+59
What is the Tangent Line to Circle Theorem?
The Tangent Line to Circle Theorem states that a line is tangent to a circle if and only if it's perpendicular to the circle's radius.
What is a straight line that just touches a circle in one place called?
A straight line touching a circle is called a tangent. The following is the image of a tangent to a circle with center C and radius AC. The tangent touches the circle at only one point - A. visit our page: balajidentalhospital .com
A line that intersects a circle at exactly one point?
Such a line is called a tangent line or a tangent to the circle. [Tangent is Latin for touching-- a tangent line touches the circle at just one point. ]
Where is the tangent secant angle on a circle?
The tangent secant angle is the angle between the tangent to a circle and the secant, when the latter is extended.
How many tangents can be drawn to a circle containing a point inside a circle?
No tangent No tangent
How do you find the tangent of a circle?
a tangent is a line that touches the circle at only ONE point
Definition of tangent in a circle?
A tangent to a circle is a line from a point outside the circles which touches the circle at a single point.
