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What is the point of contact between the tangent line y -3x -5 equals 0 and the circle x2 plus y2 -2x plus 4y -5 equals 0?
If: y -3x -5 = 0
Then: y = 3x +5
If: y^2 = (3x +5)^2
Then: y^2 = 9x^2 +30x +25
If: x^2 +y^2 -2x +4y -5 = 0
Then: x^2 +9x^2 +30x +25 -2x +12x +20 -5 = 0
Collecting like terms: 10x^2 +40x +40 = 0
Dividing all terms by 10: x^ +4x +4 = 0
Factorizing the above: (x +2)(x +2) = 0 meaning that x = -2
By substitution of x = -2 into original equations contact is made at: (-2, -1)
What else can I help you with?
What is the solution when y equals 2x plus 1 is a tangent to the circle 5y2 plus 5x2 equals 1?
If y = 2x+1 is a tangent line to the circle 5y^2 +5x^2 = 1 then the point of contact is at (-2/5, 1/5) because it has equal roots
What is the point of contact when the tangent line y -3x -5 equals 0 touches 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 x^2 +y^2 -2x +4y -5 = 0 at the coordinate of (-2, -1) on the coordinated grid.
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 point of contact between the line y equals x plus 4 and the circle x2 plus y2 -8x plus 4y equals 30?
Equations: y = x+4 and x^2 +y^2 -8x +4y = 30 It appears that the given line is a tangent line to the given circle and the point of contact works out as (-1, 3)
What is the relationship between the length of a tangent and a secant?
The relationship between the length of a tangent and a secant in a circle can be described using the tangent-secant theorem. According to this theorem, if a tangent segment is drawn from a point outside the circle to a point of tangency, and a secant segment is drawn from the same external point to intersect the circle at two points, then the square of the length of the tangent segment equals the product of the lengths of the entire secant segment and its external segment. Mathematically, if ( T ) is the length of the tangent and ( S ) is the length of the secant, the relationship can be expressed as ( T^2 = S \cdot (S - P) ), where ( P ) is the length of the part of the secant inside the circle.
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.
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?
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)
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
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.
What is the tangent line equation when it makes contact with the circle x2 plus y2 -x -31 equals 0 at -2 5 on the Cartesian plane?
Equation of circle: x^2 +y^2 -x -31 = 0 Completing the squares: (x-0.5)^2 +y^2 = 31.25 Center of circle: ( 0.5, 0) Point of contact: (-2, 5) Slope of radius: (0-5)/(0.5--2) = -2 Slope of tangent line: 0.5 Tangent line equation: y-5 = 0.5(x--2) => y = 0.5x+6
What is cotangent 32 equals tangent x?
Cotangent 32 equals tangent 0.031
What is the tangent equation of the circle x2 plus 10x plus y2 -2y -39 equals 0 at the coordinate of 3 2?
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) Point of contact: (3, 2) Slope of radius: 1/8 Slope of tangent: -8 Tangent equation: y-2 = -8(x-3) => y = -8x+26
