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What are the possible values of k if the line y equals 2x plus k meets the curve of y equals x squared -2x -7 at 2 distinctive points or at only 1 point?
Wiki User
∙ 8y ago
The two lines are y = 2x + k and y = x² - 2x - 7
Which means they meet at:
2x + k = x² - 2x - 7
→ x² - 4x - (k+7) = 0
This can be solved using the formula for quadratics:
x = (- -4 ± √((-4)² - 4×1×-(k+7)))/2
= 2 ± √(4 + k + 7)
= 2 ± √(k + 11)
This has one solution when the determinant (the part in the square root) is 0, ie
k + 11 = 0
→ k = -11
If the determinant is positive, there are two solutions, ie
k + 11 > 0
→ k > -11
Thus the there are two distinctive points if k > -11, and only 1 point if k = -11.
Wiki User
∙ 8y ago
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What is the length of the line y equals 8 -x that meets the curve of y equals x squared plus 4x plus 2 at two distinctive points?
7*sqrt(2) = 9.899 to 3 dp
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The points of intersection are: (7/3, 1/3) and (3, 1)
What are the points of intersection of 3x -2y -1 equals 0 with 3x squared -2y squared equals -5 on the Cartesian plane?
Points of intersection work out as: (3, 4) and (-1, -2)
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They work out as: (-3, 1) and (2, -14)
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)
What is the length of the line y equals 8 -x that meets the curve of y equals x squared plus 4x plus 2 at two distinctive points?
7*sqrt(2) = 9.899 to 3 dp
What are the points of intersection of the line x -y equals 2 with x squared -4y squared equals 5?
The points of intersection are: (7/3, 1/3) and (3, 1)
What are the points of intersection of 3x -2y -1 equals 0 with 3x squared -2y squared equals -5 on the Cartesian plane?
Points of intersection work out as: (3, 4) and (-1, -2)
Where are the points of intersection of the equations 4y squared -3x squared equals 1 and x -2y equals 1?
The points of intersection of the equations 4y^2 -3x^2 = 1 and x -2 = 1 are at (0, -1/2) and (-1, -1)
What are the possible points of contact when the line 2y -x equals 0 meets the curve x squared plus y squared equals 20?
If: 2y-x = 0 then 4y^2 = x^2 So : 4y^2 +y^2 = 20 or 5y^2 = 20 or y^2 = 4 Square rooting both sides: y = -2 or y = 2 Therefore possible points of contact are at: (4, 2) and (-4. -2)
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 are points of intersection of the line 3x -y equals 5 with the curve of 2x squared plus y squared equals 129?
Straight line: 3x-y = 5 Curved parabola: 2x^2 +y^2 = 129 Points of intersection works out as: (52/11, 101/11) and (-2, -11)
What are the possible values of k if the line y equals 2x plus k with the curve of y equals x squared -2x -7 at 2 distintive points or at only 1 point?
It works out that k must be greater than -11 or k must equal -11
What are the points of intersection of the parabolas of y equals 4x squared -12x -3 and y equals x squared plus 11x plus 5 on the Cartesian plane?
The points are (-1/3, 5/3) and (8, 3).Another Answer:-The x coordinates work out as -1/3 and 8Substituting the x values into the equations the points are at (-1/3, 13/9) and (8, 157)
What is y equals x squared?
it will form a parabola on the graph with the vertex at point (0,0) and points at (1,1), (-1,1), (2,4), (-2,4)......
What are the coordinates of the straight line of y equals 5x plus 10 that meets the parabola of y equals x squared plus 4 at points A and B?
(6, 40) and (-1, 5)
What are the points of contact between the line 3x -2y equals 1 and the curve 3x squared -2y squared plus 5 equals 0?
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