If: x +y = 7 then y = 7 -x
IF: x^2 +y^2 = 25 then x^2 +(7 -x)^2 -25 = 0
Removing brackets: x^2 +49 -14x +x^2 -25 = 0
Collecting like terms: 2x^2 -14x +24 = 0
Dividing all terms by 2: x^2 -7x +12 = 0
Factorizing: (x -3)(x -4) = 0 => x = 3 or x = 4
By substitution points of intersection are at: (3, 4) and (4, 3)
Using distance formula: length of line from (3, 4) to (4, 3) = square root of 2
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
If: x-2y = 8 and xy = 24 Then: x = 8+2y and y(8+2y) = 24 => 2y^2+8y-24 = 0 Solving the above quadratic equation: y = 2 or y = -6 Points of intersection of the line with the curve: (-4, -6) and (12, 2) Length of line: square root [(-4-12)^2 plus (-6-2)^2] = square root of 320 which is about 18 units rounded to the nearest integer
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.
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
7*sqrt(2) = 9.899 to 3 dp
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
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.
If: x-2y = 8 and xy = 24 Then: x = 8+2y and y(8+2y) = 24 => 2y^2+8y-24 = 0 Solving the above quadratic equation: y = 2 or y = -6 Points of intersection of the line with the curve: (-4, -6) and (12, 2) Length of line: square root [(-4-12)^2 plus (-6-2)^2] = square root of 320 which is about 18 units rounded to the nearest integer
If: y = 4x2-2x-1 and y = -2x2+3x+5 Then the length of the line works out as: 65/18 or 3.6111 ... recurring decimal 1
Do a line integral.
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.
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
7*sqrt(2) = 9.899 to 3 dp
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)
It is (-0.3, 0.1)
tan A = (sin A) / (cos A) tan (A)= opposite side length/adjacent side length A is an angle measurement; amount of degrees or radians. If a line is tangent to a curve, it only touches the curve at one point. looks like )| but the line is touching the curve. In a circle, the tangent line touches the circle at one point and is perpinducular to the circle's radius if it is touching that same point.
You can measure the length of a curved line by using a flexible measuring tape following the curve or by breaking it down into smaller straight segments and adding them up. Another option is to use a formula that calculates the arc length of a curve based on its equation and limits.