Finding the Length of a Chord on a Circle

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Homework Help Overview

The discussion revolves around finding the length of a chord that a given circle cuts off from a specified straight line, as well as determining the equation of a circle with this chord as its diameter. The problem involves concepts from geometry and algebra, particularly related to circles and lines in a coordinate system.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore methods for calculating the length of the chord, questioning whether there are specific formulas applicable to the situation. There is discussion about using the distance from the center of the circle to the chord and the intercepts of the line.

Discussion Status

Some participants have suggested finding the points of intersection between the circle and the line as a means to determine the chord's length. Others have raised questions about the relationship between the intercepts of the line and the radius of the circle, indicating a lack of consensus on the best approach.

Contextual Notes

Participants note that the distance of the chord from the center of the circle is not explicitly given, which may complicate the calculations. The original poster and others are trying to navigate the implications of the given equations and the geometry involved.

Dumbledore211
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Homework Statement


Find the length of the chord which the circle 3x^2+3y^2-29x-19y+56=0 cuts off from the straight line x-y+2+=0. Find the equation of the circle with this chord as diameter


Homework Equations


x^2+y^2+2gx+2fy+c=0


The Attempt at a Solution


I can solve the second part of the question very easily. What I am really finding difficult is trying to construct a method of calculating the length of the chord. Is there any formula or equation for it?
 
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Dumbledore211 said:

Homework Statement


Find the length of the chord which the circle 3x^2+3y^2-29x-19y+56=0 cuts off from the straight line x-y+2+=0. Find the equation of the circle with this chord as diameter


Homework Equations


x^2+y^2+2gx+2fy+c=0


The Attempt at a Solution


I can solve the second part of the question very easily. What I am really finding difficult is trying to construct a method of calculating the length of the chord. Is there any formula or equation for it?

Think about it. If you were dealing with simple geometry where you were given the radius of circle and the distance of chord from the centre, how do you find the length of chord?
 
Pranav-Arora said:
Think about it. If you were dealing with simple geometry where you were given the radius of circle and the distance of chord from the centre, how do you find the length of chord?
With the information given, it might be easier just to find the intercepts.
 
@haruspex I don't precisely get what you are trying to put across. Are you suggesting that I should find the intercepts of the straight line as well as the radius of the circle from the given two equations. Tell me how the intercepts of the straight line relate with the radius of the circle??
 
@Pranav Arora But the distance of chord from the centre is not given..
 
Dumbledore211 said:
@Pranav Arora But the distance of chord from the centre is not given..

You can find it...You have the equation of chord and coordinate of center.
 
Dumbledore211...Simply find the points of intersection of the circle with the straight line .This will give you two points in the plane .In the first part you have to find the length of the chord which is nothing but the distance between these two points .
 
Dumbledore211 said:
@haruspex I don't precisely get what you are trying to put across. Are you suggesting that I should find the intercepts of the straight line as well as the radius of the circle from the given two equations. Tell me how the intercepts of the straight line relate with the radius of the circle??

If you have the intercepts you can use it to find the position of center of the new circle. ED- And the length as Tanya pointed out above(crossed posts)
 
Thank you, Tanya Sharma. I finally got the answer which is 4(2)^1/2
 
  • #10
Dumbledore211 said:
Thank you, Tanya Sharma. I finally got the answer which is 4(2)^1/2

Well done...
 

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