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What is the point of contact when the tangent line y equals 3x plus 5 touches the circle x squared plus y squared -2x plus 4y -5 equals 0 on the Cartesian plane?
Wiki User
∙ 7y ago
Equation of the circle: x^2 +y^2 -2x +4y -5 = 0
Completing the squares: (x-1)^2 +(y+2)^2 = 10
Centre of circle: (1, -2)
Slope of the radius: -1/3 because it is perpendicular to the tangent line
Equation of the radius: y --2 = -1/3(x-1) => 3y = -x-5
Solving the simultaneous equations of: 3y = -x-5 and y = 3x+5 => x = -2, y = -1
Therefore the point of contact is at: (-2, -1)
Wiki User
∙ 7y ago
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What is the tangent equation of the circle 2x squared plus 2y squared -8x -5y -1 that touches the point of 1 -1 on the Cartesian plane?
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
What does a Tangent look like?
Usually a straight line that touches a curve at one point. At the point of contact, the tangent is perpendicular to the radius of curvature.
What is the equation of the tangent line that touches the circle x squared plus y squared -6x plus 4y equals 0 at the point of 6 -4 on the Cartesian plane?
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
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 osculator?
An osculator is a surface that touches (or kisses) another so that they share a tangent at the point of contact.
What is the tangent equation of the circle 2x squared plus 2y squared -8x -5y -1 that touches the point of 1 -1 on the Cartesian plane?
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
What does a Tangent look like?
Usually a straight line that touches a curve at one point. At the point of contact, the tangent is perpendicular to the radius of curvature.
What is the equation of the tangent line that touches the circle x squared plus y squared -6x plus 4y equals 0 at the point of 6 -4 on the Cartesian plane?
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
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 is the point of contact when the tangent line y equals x plus c touches the curve y equals 3x -x -5x squared?
-2
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 tangent of the curve?
A tangent is a line which touches, but does not cross, a curved line.
What is osculator?
An osculator is a surface that touches (or kisses) another so that they share a tangent at the point of contact.
What is meant by tangent to a curve at a point?
It is a straight line that touches the curve such that the line is perpendicular to the radius of the curve at the point of contact.
A line that touches a circle?
Tangent
What t-word is define in geometry as a straight line that touches a curve but continues on with crossing it?
A tangent line touches a curve or the circumference of a circle at just one point.
What is the tangent of a circle?
A tangent is a straight line that touches a circle's circumference at one point
