Circle problem

  • #1
Dumbledore211
111
1

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????
 

Answers and Replies

  • #2
Saitama
4,244
93

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?
 
  • #3
haruspex
Science Advisor
Homework Helper
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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.
 
  • #4
Dumbledore211
111
1
@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??
 
  • #5
Dumbledore211
111
1
@Pranav Arora But the distance of chord from the centre is not given..
 
  • #6
Enigman
666
307
@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.
 
  • #7
Tanya Sharma
1,540
135
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 .
 
  • #8
Enigman
666
307
@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)
 
  • #9
Dumbledore211
111
1
Thank you, Tanya Sharma. I finally got the answer which is 4(2)^1/2
 
  • #10
Tanya Sharma
1,540
135
Thank you, Tanya Sharma. I finally got the answer which is 4(2)^1/2

Well done...
 

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