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What is the length of the tangent line from the coordinate of 9 0 to a point where it touches the circle of x2 plus 8x plus y2 -9 equals 0?
Wiki User
∙ 6y ago
Circle equation: x^2 +8x +y^2 -9 = 0
Completing the square: (x+4)^2 +y^2 = 25
Center of circle: (-4, 0)
Radius of circle: 5
Distance from (-4, 0) to (9, 0) = 13 which will be the hypotenuse of a right triangle
Length of tangent line using Pythagoras; theorem: 13^2 -5^2 = 144
Therefore length of tangent line is the square root of 144 = 12 units
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoThe tangents have a length of 12 units.
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What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
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 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?
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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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What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
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 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?
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What is the tangent equation of the circle x2 plus 10x plus y2 -2y -39 equals 0 at the coordinate of 3 2?
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What is the equation for a circle with its center at the origin and a tangent whose equation is y equals 7?
x2 + y2 = 49
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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?
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What is the distance from a defined point on the x axis to the centre of circle x2 plus y2 -2x -6y plus 5 equals 0 when its tangent is at 3 4 on the Cartesian plane?
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 contact point: (3, 4) Slope of radius: ((3-4)/(1-3) = 1/2 Slope of tangent line: -2 Equation of tangent line: y-4 = -2(x-3) => y = -2x+10 Equation tangent rearranged: 2x+y = 10 When y equals 0 then x = 5 or (5, 0) as a coordinate Distance from (5, 0) to (1, 3) = 5 using the distance formula
