Question:
A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.
A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.
Updated On: Sep 24, 2024
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Correct Answer: 16
Solution and Explanation
The correct answer is 16
As slope of line joining (1, 2) and (3, 6) is 2 given diameter is parallel to side
Hence, \(a = \sqrt{(3−1)^2+(6−2)^2}\)
\(= \sqrt{20}\)
Thereafter, \(\frac{b}{2} = \frac{4}{\sqrt5}\)
\(⇒ b = \frac{8}{\sqrt5}\)
So, the Area ab \(= 2 \sqrt5 . \frac{8}{\sqrt5}\)
= 16
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Concepts Used:
Coordinate Geometry
Coordinate geometry, also known as analytical geometry or Cartesian geometry, is a branch of mathematics that combines algebraic techniques with the principles of geometry. It provides a way to represent geometric figures and solve problems using algebraic equations and coordinate systems.
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.
The central idea in coordinate geometry is to assign numerical coordinates to points in a plane or space, which allows us to describe their positions and relationships using algebraic equations. The most common coordinate system is the Cartesian coordinate system, named after the French mathematician and philosopher René Descartes.