Search results
Results From The WOW.Com Content Network
This can be done with calculus, or by using a line that is parallel to the axis of symmetry of the parabola and passes through the midpoint of the chord. The required point is where this line intersects the parabola. [e] Then, using the formula given in Distance from a point to a line, calculate the perpendicular distance from this point to the ...
the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line y = − x / m . {\displaystyle y=-x/m\,.} This distance can be found by first solving the linear systems
For parallel chords the slope is constant and the midpoints of the parallel chords lie on the line = . Consequence: for any pair of points P , Q {\displaystyle P,Q} of a chord there exists a skew reflection with an axis (set of fixed points) passing through the center of the hyperbola, which exchanges the points P , Q {\displaystyle P,Q} and ...
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let ( m , n ) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point ( x 0 , y 0 ).
a, b, and c are related to the slope of the line, such that the direction vector (a, b, c) is parallel to the line. Parametric equations for lines in higher dimensions are similar in that they are based on the specification of one point on the line and a direction vector.
Such a parametric equation is called a parametric form of the solution of the system. [10] The standard method for computing a parametric form of the solution is to use Gaussian elimination for computing a reduced row echelon form of the augmented matrix.
It has also been called Sen's slope estimator, [1] [2] slope selection, [3] [4] the single median method, [5] the Kendall robust line-fit method, [6] and the Kendall–Theil robust line. [7] It is named after Henri Theil and Pranab K. Sen , who published papers on this method in 1950 and 1968 respectively, [ 8 ] and after Maurice Kendall ...
a pencil of parallel lines, if the given lines are parallel or the pencil of hyperbolas, which have the given lines as asymptotes. For example, the product of the coordinate axes variables yields the pencil of hyperbolas x y − c = 0 , c ≠ 0 {\displaystyle xy-c=0,\ c\neq 0} , which have the coordinate axes as asymptotes.