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What is the point of contact when the tangent line y equals 2x touches the curve x2 plus y2 -8x -y plus 5 equals 0?
If: y = 2x then y^2 = 4x^2
If: x^2 +y^2 -8x -y +5 = 0 then x^2 +4x^2 -8x -2x +5 = 0
Collecting like terms: 5x^2 -10x +5 = 0
Dividing all terms by 5: x^2 -2x +1 = 0
Factorizing the above: (x -1)(x -1) = 0 meaning x = 1
By substitution into the original equation contact is made at: (1, 2)
What else can I help you with?
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 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 do you call a straight line which touches a curve but continues without crossing it?
A straight line that touches a curve but continues without crossing it is called a "tangent." At the point of contact, the tangent line has the same slope as the curve, indicating that it just grazes the curve rather than intersecting it.
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.
How do you find the point of tangency?
A tangent is an object, like a line, which touches a curve. The tangent only touches the curve at one point. That point is called the point of tangency. The tangent does not intersect (pass through) the curve.
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 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 do you call a straight line which touches a curve but continues without crossing it?
A straight line that touches a curve but continues without crossing it is called a "tangent." At the point of contact, the tangent line has the same slope as the curve, indicating that it just grazes the curve rather than intersecting it.
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 tangent of the curve?
A tangent is a line which touches, but does not cross, a curved line.
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
How do you find the point of tangency?
A tangent is an object, like a line, which touches a curve. The tangent only touches the curve at one point. That point is called the point of tangency. The tangent does not intersect (pass through) the curve.
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 a point of tangency?
It is the point at which a tangent touches a curve.
What is the name given to a straight line that touches a curve?
In geometry a straight line that touches a curve is called a tangent.
What is a straight line that touches a curve but continues on with crossing it?
A tangent line.
What t word is defined in geometry as a straight line that touches a curve but continues on with out crossing it?
The term you're looking for is "tangent." In geometry, a tangent is a straight line that touches a curve at a single point, known as the point of tangency, and continues on without crossing the curve at that point. Tangents are often discussed in relation to circles and other curves, where they represent the instantaneous direction of the curve at the point of contact.
