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What are the curve and line coordinates for x square plus y square plus 4x plus 6y - 40 equals 0 and x - y equals 10?
I presume you want the points where the circle x2 + y2 + 4x + 6y - 40 = 0 and the line x - y = 10 meet.
x - y = 10
=> y = x - 10
Substitute into circle equation:
x2 + y2 + 4x + 6y - 40 = 0
=> x2 + (x - 10)2 + 4x + 6(x - 10) - 40 = 0
=> x2 + x2 - 20x + 100 + 4x + 6x - 60 - 40 = 0
=> 2x2 - 10x = 0
=> 2x(x - 5) = 0
=> x = 0 or 5
=> y = -10 or -5 respectively
The line meets the circle at the points (0, -10) and (5, -5).
Another method with the same result:
Equation 1: x2+y2+4x+6y-40 = 0
Equation 2: x-y = 10 => x = 10+y
Substitute Equation 2 into Equation 1:
(10+y)(10+y)+y2+4(10+y)+6y-40 = 0
100+20y+y2+y2+40+4y+6y-40 = 0
Collect like terms:
2y2+30y+100 = 0 => (2y+20)(y+5) = 0
y = -10 or y = -5
Substitute the above values into Equation 2:
When y = -10, x = 0
When y = -5, x = 5
Therefore the coordinates are: (0,-1) and (5,-5)
What else can I help you with?
What are the coordinates and length of the straight line of y equals 5x plus 10 that meets the parabola of y equals x square plus 4 at two points?
Coordinates: (-1, 5) and (6, 40) Length of line: 7 times the square root of 26 which is 35.693 to 3 d.p.
Midpoint of curve or line segment?
Average the x and y (and z if there is one) coordinates to find a midpoint of a line.
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 point of cotact when the line y equals 2x plus 5 over 4 meets the curve y squared equals 10xa?
If you mean a line of y = 2x+5/4 and a curve of y^2 = 10x Then it works out that the line touches the curve at: (5/8, 5/2)
How do you find the value of c when the straight line y equals x plus c touches the curve y equals 3 -x -5x squared?
-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 are the coordinates and length of the straight line of y equals 5x plus 10 that meets the parabola of y equals x square plus 4 at two points?
Coordinates: (-1, 5) and (6, 40) Length of line: 7 times the square root of 26 which is 35.693 to 3 d.p.
Midpoint of curve or line segment?
Average the x and y (and z if there is one) coordinates to find a midpoint of a line.
What points are on the line given by the equation y equals x?
Y Equals X PointsAll points that has the same y coordinates as x coordinates are on the y=x line.
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 point of cotact when the line y equals 2x plus 5 over 4 meets the curve y squared equals 10xa?
If you mean a line of y = 2x+5/4 and a curve of y^2 = 10x Then it works out that the line touches the curve at: (5/8, 5/2)
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)
How do you find the value of c when the straight line y equals x plus c touches the curve y equals 3 -x -5x squared?
-2
How can we find the coordinates of x in the intersection of line and curve?
For example, the equation of a line: y = ax + b. the equation of a curve: y = cx2 + dx + e ax + b = cx2 + dx + e (solve for x)
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 coordinates for -4x plus 9y equals 0?
-4x + 9y = 0 is the equation of a line in the Cartesian plane and the coordinates of any of the infinite number of points on that line will satisfy the equation.
How can you prove in at least two ways that the straight line of y equals 2x plus 5 over 4 is a tangent to the curve of y square equals 10x?
Combine the two equations together to give a quadratic equation in the form of:- 4x2 - 5x + 25/16 = 0 The solution to this is x = 5/8 or x = 5/8 meaning that it has equal roots therefore the line is tangent to the curve. The discriminant of b2 - 4ac = 0 also proves that the quadratic equation has two equal roots which makes the line tangent to the curve. Further proof can be found by plotting the straight line and curve graphically.
