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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?
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)
What else can I help you with?
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 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.
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
A line that touches the circle at one point?
A tangent is a line that touches a circle at exactly one point. It is perpendicular to the radius at the point of contact.
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 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.
What is osculator?
An osculator is a surface that touches (or kisses) another so that they share a tangent 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.
