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What are the solutions to the equations when the line x plus y equals -0.25 meets the curve y equals x squared?
Equation of line: x +y = -0.25 or x +y = -1/4
Equation of curve: y = x^2
If: x +y = -1/4 then y = -1/4 -x
If: y = x^2 then x^2 = -1/4 -x or 4x^2 = -1 -4x
Transposing terms: 4x^2 +4x +1 = 0
Factorizing the above: (2x+1)(2x+1) = 0 meaning x = -1/2
Therefore by substitution solutions are: x = -1/2 and y = 1/4
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What are the points of contact between the line 3x -2y equals 1 and the curve 3x squared -2y squared plus 5 equals 0?
Equations: 3x-2y = 1 and 3x^2 -2y^2 +5 = 0 By combining the equations into one single quadratic equation and solving it the points of contact are made at (3, 4) and (-1, -2)
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 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 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 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
Where are the points of contact when the line 2x plus 5 equals 4 crosses the curve y squared equals x plus 4 on the Cartesian plane?
The two solutions are (x, y) = (-0.5, -sqrt(3.5)) and (-0.5, sqrt(3.5))
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 are the coordinates of the line x-y equals 2 that intersects the of curve x squared-4y squared equals 5?
If you mean the coordinates of the line x-y = 2 that intersects the curve of x2-4y2 = 5 Then the coordinates work out as: (3, 1) and (7/3, 1/3)
What is the exact point of contact when the curve of y equals x squared -10x plus 13 touches the curve of y equals x squared -4x plus 7 showing work?
If: y = x^2 -10x +13 and y = x^2 -4x +7 Then: x^2 -10x +13 = x^2 -4x +7 Transposing terms: -6x +6 = 0 => -6x = -6 => x = 1 Substituting the value of x into the original equations point of contact is at: (1, 4)
What are the points of intersection of the line y equals -8-3x with the curve y equals -2-4x-x squared?
They work out as: (-3, 1) and (2, -14)
What is the length of the line x -y equals 2 that spans the curve x squared - 4y squared equals 5?
The line x-y = 2 intersects with the curve x^2 -4y^2 = 5 at (2.5, 1/3) and (3, 1) and by using the distance formula its length is 5/6
Where are the points of contact when the line 3x -y equals 5 passes through the curve 2x squared plus y squared equals 129?
It works out that line 3x-y = 5 makes contact with the curve 2x^2 +y^2 = 129 at (52/11, 101/11) and (-2, -11)
