Finding the Length of a Chord on a Circle

[Dumbledore211]

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?

 

[Saitama]

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?

 

[haruspex]

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.

 

[Dumbledore211]

@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??

 

[Dumbledore211]

@Pranav Arora But the distance of chord from the centre is not given..

 

[Enigman]

@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.

 

[Tanya Sharma]

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 .

 

[Enigman]

@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)

 

[Dumbledore211]

Thank you, Tanya Sharma. I finally got the answer which is 4(2)^1/2

 

[Tanya Sharma]

Thank you, Tanya Sharma. I finally got the answer which is 4(2)^1/2

Well done...