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What is the point of contact when the tangent line y equals 20 -2x touches the curve x squared plus y squared equals 80?
If: y = 20 -x and x^2 +y^2 = 80
Then: x^2 +(20-x)^2 = 80
Multiplying out the brackets: x^2 +400 -80x +4x^2 = 80
Transposing terms: 5x^2 +320 -80x = 0
Divide all terms by five: x^2 +64 -16x = 0
Factorizing: (x-8)(x-8) = 0 => x = 8 and x = 8
By substitution point of contact is at: (8, 4)
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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 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
How do you solve secant squared divided by tangent?
In trig, the secant squared divided by the tangent equals the hypotenuse squared divided by the product of the opposite and adjacent sides of the triangle.Details: secant = hypotenuse/adjacent (H/A) and tangent = opposite/adjacent (A/O);Then secant2/tangent = (H2/A2)/(O/A) = H2/A2 x A/O = H2/AO.
What are the possible value of k when the line y equals x plus k is a tangent to the circle x squared plus y squared equals 25?
They are +/- 5*sqrt(2)
What is the point of contact when the line y equals 2x plus 1.25 touches the curve y squared equals 10x?
Combine the equations together and using the quadratic equation formula it works out that the point of contact is at (5/8, 5/2)
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
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)
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 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 the equation of the tangent line that touches the circle x squared plus y squared -8x -16y -209 equals 0 at a coordinate of 21 and 8?
Circle equation: x^2 +y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius of circle 17 Slope of radius: 0 Perpendicular tangent slope: 0 Tangent point of contact: (21, 8) Tangent equation: x = 21 passing through (21, 0)
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
How do you solve secant squared divided by tangent?
In trig, the secant squared divided by the tangent equals the hypotenuse squared divided by the product of the opposite and adjacent sides of the triangle.Details: secant = hypotenuse/adjacent (H/A) and tangent = opposite/adjacent (A/O);Then secant2/tangent = (H2/A2)/(O/A) = H2/A2 x A/O = H2/AO.
What is the value of c when y equals x plus c is a tangent to the curve y equals 3 -x -5x squared hence finding the point of contact of the line with the curve showing work?
-2
What is the point of contact when the tangent line y -3x -5 equals 0 touches the circle x2 plus y2 -2x plus 4y -5 equals 0?
It works out that the tangent line of y -3x -5 = 0 makes contact with the circle x^2 +y^2 -2x +4y -5 = 0 at the coordinate of (-2, -1) on the coordinated grid.
What are the possible value of k when the line y equals x plus k is a tangent to the circle x squared plus y squared equals 25?
They are +/- 5*sqrt(2)
Where is the point of contact when the line y equals 2x plus 1.25 touches the curve y squared equals 10x?
If y = 2x +10 and y^2 = 10x then by forming a single quadratic equation and solving it the point of contact is made at (5/8, 5/2)
What is the point of contact when the line y equals 2x plus 1.25 touches the curve y squared equals 10x?
Combine the equations together and using the quadratic equation formula it works out that the point of contact is at (5/8, 5/2)
