What is orthogonal trajectory of parabola?

orthogonal trajectory, family of curves that intersect another family of curves at right angles (orthogonal; see figure). Solving this for the orthogonal curve gives the solution y2 + (x2/2) = k, which represents a family of ellipses (shown in red in the figure) orthogonal to the family of parabolas.

What are the orthogonal trajectories of the family of curves?

The orthogonal trajectories are the curves that are perpendicular to the family everywhere. In other words, the orthogonal trajectories are another family of curves in which each curve is perpendicular to the curves in original family.

How do you find orthogonal trajectories in polar coordinates?

Orthogonal Trajectories in Polar Co-ordinates If φ and φ’ denote the angles which the tangent to the given curve and the trajectory at the point of intersection (r, θ), make with the radius vector to the common point, φ ~ φ’ = (π/2) and so tanφ = – cotφ’. − 1 r d r d θ f o r r d θ d r i .

What is oblique trajectory?

OBLIQUE TRAJECTORIES A curve which intersects the curves of the given family at a constant angle α ≠ 90º is called an oblique trajectory of the given family.

How do you know if two curves are orthogonal?

Two curves are said to be orthogonal if their tangent lines are perpendicular at every point of intersection. Two families of curves are said to be orthogonal if every curve in one family is orthogonal to every curve in the other family.

How do you find the orthogonal line of a curve?

Is Matrix orthogonal?

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix. Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

What is the use of orthogonal trajectories?

Orthogonal trajectories are used in mathematics for example as curved coordinate systems (i.e. elliptic coordinates) or appear in physics as electric fields and their equipotential curves. If the trajectory intersects the given curves by an arbitrary (but fixed) angle, one gets an isogonal trajectory.

What is orthogonal in maths?

Orthogonal is commonly used in mathematics, geometry, statistics, and software engineering. Most generally, it’s used to describe things that have rectangular or right-angled elements. More technically, in the context of vectors and functions, orthogonal means “having a product equal to zero.”