If: y = 3x +1 then y^2 = 9x^2 +6x +1
If: y^2 +x^2 = k then y^2 = k -x^2
So: 9x^2 +6x +1 = k -x^2
Transposing terms: 10x^2 +6x +(1 -k) = 0
Using the discriminant: 6^2 -4*10*(1 -k) = 0
Solving the discriminant: k = 1/10
k = 0.1
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.
If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x then it works out that when x = 5/8 then y = 5/2
k = 0.1
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.
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
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.
It is (-0.3, 0.1)
If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x then it works out that when x = 5/8 then y = 5/2
k = 0.1
A tangent is a line which touches, but does not cross, a curved line.
Tangent:In geometry, the tangent line (or simply the tangent) is a curve at a given point and is the straight line that "just touches" the curve at that point. As it passes through the point where the tangent line and the curve meet the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point.Chord:A chord of a curve is a geometric line segment whose endpoints both lie on the outside of the circle.
If: y = kx+1 is a tangent to the curve y^2 = 8x Then k must equal 2 for the discriminant to equal zero when the given equations are merged together to equal zero.
y=0. note. this is a very strange "curve". If y=0 then any value of x satisfies the equation, leading to a curve straight along the y axis. For any non-zero value of y the curve simplifies to y = -x. The curve is not differentiable at the origin.
A line tangent to a curve, at a point, is the closest linear approximation to how the curve is "behaving" near that point. The tangent line is used to estimate values of the curve, near that point.
-2
By differentiating the answer and plugging in the x value along the curve, you are finding the exact slope of the curve at that point. In effect, this would be the slope of the tangent line, as a tangent line only intersects another at one point. To find the equation of a tangent line to a curve, use the point slope form (y-y1)=m(x-x1), m being the slope. Use the differential to find the slope and use the point on the curve to plug in for (x1, y1).
(2, -2)