Let the abscissa of the point of intersection of the lines (x)/(a)+(y)/(b)=2 and (x)/(b)+(y)/(a)

step 1 In this problem we have been given, let the abscessa of the point of intersection of the lines,

Let the abscissa of the point of intersection of the lines...

Let the abscissa of the point of intersection of the lines $\frac{x}{a}+\frac{y}{b}=2$ and $\frac{x}{b}+\frac{y}{a}=2$ be $c$. Then (a) ordinate of the point of intersection of the lines is $\frac{c}{a+b}$ (b) ordinate of the point of intersection of the lines is $\mathrm{c}$. (c) $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. (d) $\mathrm{a}, \mathrm{c}, \mathrm{b}$ are in $\mathrm{H.P}$.

Let the abscissa of the point of intersection of the lines $\frac{x}{a}+\frac{y}{b}=2$ and $\frac{x}{b}+\frac{y}{a}=2$ be $c$. Then
(a) ordinate of the point of intersection of the lines is $\frac{c}{a+b}$
(b) ordinate of the point of intersection of the lines is $\mathrm{c}$.
(c) $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P.
(d) $\mathrm{a}, \mathrm{c}, \mathrm{b}$ are in $\mathrm{H.P}$.

Key Concepts

Harmonic Progression (H.P.)

A harmonic progression is a sequence of numbers formed when the reciprocals of the numbers are in arithmetic progression. It introduces a non-linear relationship between consecutive terms and is an important concept in series and mathematical analysis, particularly when exploring properties that differ from those of arithmetic sequences.

Intersection of Lines

When two lines in a plane intersect, they share a common point whose coordinates satisfy both linear equations simultaneously. This concept is fundamental in coordinate geometry and is often explored by solving a system of equations where the abscissa (x?coordinate) and ordinate (y?coordinate) are determined by equating the expressions defining the lines.

Abscissa and Ordinate

In coordinate geometry, any point in the Cartesian plane is described by an ordered pair where the first coordinate, called the abscissa, represents the horizontal distance from the origin, and the second coordinate, called the ordinate, represents the vertical distance. Understanding these terms is critical for analyzing intersections and relationships between points on the plane.

Arithmetic Progression (A.P.)

An arithmetic progression is a sequence of numbers in which the difference between any two successive members is a constant, known as the common difference. This concept is widely used in algebra and number theory to describe and analyze linear relationships within sequences or sets of numbers.

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