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Circle equation: x^2 +y^2 -8x -16y -209 = 0

Completing the squares: (x-4)^2 +(y-8)^2 = 289

Centre of circle: (4, 8)

Radius of circle 17

Slope of radius: 0

Perpendicular tangent slope: 0

Tangent point of contact: (21, 8)

Tangent equation: x = 21 passing through (21, 0)

Q: What is the equation of the tangent line that touches the circle x squared plus y squared -8x -16y -209 equals 0 at a coordinate of 21 and 8?

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A tangent line touches a curve or the circumference of a circle at just 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. ]

Is calleda tangent line. Is called a tangent line

A tangent line.

It is called a tangent.

Related questions

You need more than one tangent to find the equation of a parabola.

If you mean: 2x^2 +2y^2 -8x -5y -1 = 0 making contact at (1, -1) Then the tangent equation in its general form works out as: 4x+9y+5 = 0

Circle equation: x^2 +y^2 -8x -16y -209 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius: 17 Slope of radius: 0 Tangent equation line: x = 21 passing through (21, 0)

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

Equation: x² + y² -6x +4y = 0 Completing the squares: (x-3)² + (y+2)² = 13 Centre of circle: (3, -2) Contact point: (6, -4) Slope of radius: -2/3 Slope of tangent: 3/2 Tangent equation: y - -4 = 3/2(x-6) => 2y - -8 = 3x-18 => 2y = 3x-26 Tangent line equation in its general form: 3x-2y-26 = 0

A tangent of a circle is a straight line that touches the circle at only one point.

A tangent is a line which touches, but does not cross, a curved line.

Tangent

-2

The tangent equation that touches the circle 2x^2 +2y^2 -8x -5y -1 = 0 at the point of (1, -1) works out in its general form as: 4x +9y +5 = 0

Equation of the curve: 2x^2 +2y^2 -8x -5y -1 = 0 Divide all terms by two: x^2 +y^2 - 4x -2.5y -0.5 = 0 Completing the squares: (x-2)^2 +(y-1.25)^2 = 6.0625 Centre of circle: (2, 1.25) Contact point: (1, -1) Slope of radius: 9/4 Slope of tangent: -4/9 Tangent equation: y--1 = -4/9(x-1) => 9y --9 = -4x+4 => 9y = -4x-5 Tangent line equation in its general form: 4x+9y+5 = 0

Equation of circle: 2x^2 +2y^2 -8x -5y -1 = 0 Divide all terms by two: x^2 +y^2 -4x -2.5 -0.5 = 0 Completing the squares: (x-2)^2 + (y-1.25)^2 = 97/16 Point of contact: (1, -1) Centre of circle: (2, 1.25) Slope of radius: 9/4 Slope of tangent: -4/9 Equation of tangent: y--1 = -4/9(x-1) => 9y--9 = -4x+4 => 9y = -4x-5 Tangent equation in its general form: 4x+9y+5 = 0