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How can you prove that the straight line of y equals x plus k is a tangent to the curve of x squared plus y squared equals 4 and only when k squared equals 8?
You don't.
Furthermore, how would you prove your not a virgin? Either way your fu'd.
Improved Answer:-
y = x+k
x2+y2 = 4
Substitute y = x+k into the bottom equation:
x2+(x+k)(x+k) = 4
x2+x2+2kx+k2 = 4
k2 = 8 so therefore:
2x2+2kx+8-4 = 0 => 2x2+2kx+4 = 0
For the straight line to be a tangent to the curve the discriminant b2-4ac of the quadratic equation must equal zero:
Hence:-
(2*k)2-4*2*4 = 0
k2 = 8
So: 4*8-4*2*4 = 0 => 32-32 = 0
Therefore the straight line y = x+k is a tangent to the curve x2+y2 = 4
What else can I help you with?
What is the value of k when the straight y equals 3x-1 is a tangent to the curve x squared plus y squared equals k?
2
What is the value of k when y equals 3x plus 1 and is a line tangent to the curve of x squared plus y squared equals k?
k = 0.1
What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
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
Straight lines that touch but don't intersect a curve?
Tangent to the 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.
At what point is the line of y equals x -4 tangent to the curve of x squared plus y squared equals 8?
(2, -2)
What is the value of k when the straight y equals 3x-1 is a tangent to the curve x squared plus y squared equals k?
2
What is the value of k when y equals 3x plus 1 and is a line tangent to the curve of x squared plus y squared equals k?
k = 0.1
What is the value of k when y equals 3x plus 1 is a line tangent to the curve of x squared plus y squared equals k hence finding the point of contact of the line to the curve?
It is (-0.3, 0.1)
What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
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
Straight lines that touch but don't intersect a curve?
Tangent to the 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.
In maths what is a tangent and what is a chord?
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.
What is the value of k in the line of y equals kx plus 1 and is tangent to the curve of y squared equals 8x?
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.
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 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 straight line that touches a curve but continues on with crossing it?
A tangent line.
