0
What is the length of the line x -y equals 10 that spans the curve x squared plus y squared plus 4x plus 6y -40 equals 0 showing work?
Wiki User
∙ 8y ago
If: x^2+y^2+4x+6y-40 = 0 and x-y =10 or as x = 10+y
Then: (10+y)^2+y^2+4(10+y)+6y-40 = 0
Thus: 100+20y+y^2+y^2+40+4y+6y-40 = 0
Collecting like terms: 2y^2+30y+100 = 0 or as y^2+15y+50 = 0
When factored: (y+5)(y+10) = 0
So: y = -5 or y = -10
By substitution equations intersect at: (0, -10) and (5, -5)
Length of line is the square root of: (5-0)^2 plus (-5--10)^2 = square root of 50
Therefore length of line is: square root of 50 or about 7.071 to three decimal places
Wiki User
∙ 8y ago
Add your answer:
Earn +20 pts
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
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 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 y equals -8-3x with the curve y equals -2-4x-x squared?
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 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
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
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 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
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 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 length of the line of y equals 17 -3x that spans the curve of y equals x squared plus 2x -7?
If you mean: y = 17-3x and y = x^2+2x-7 then the length of the line works out as 11 times square root of 10 or about 34.785 to three decimal places.
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)
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 5x plus 10 that meets the curve of y equals x squared plus 4 at two distinctive points?
The line of y = 5x+10 intersects with the curve of y = x2+4 at (6, 40) and (-1, 5) Length of the line is the square root of: (6--1)2+(40-5)2 = 7 times sq rt of 26 or 35.693 to three decimal places
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
