Finding the Centre of a Circle Passing Through Given Points (1,-2) and (4,-3)

  • Thread starter Thread starter zorro
  • Start date Start date
  • Tags Tags
    Circle
AI Thread Summary
To find the center of a circle passing through the points (1,-2) and (4,-3) while lying on the line 3x + 4y = 7, the distance from the center to both points must be equal. The initial attempt led to the equation 3x - 2y = 10, but upon solving the two equations, the correct center was identified as (3, -1/2). However, the user realized a mistake in deriving the second equation, which should have been 3x - y = 10. This correction is crucial for accurately determining the circle's center.
zorro
Messages
1,378
Reaction score
0

Homework Statement


Find the centre of the circle which passes through the points (1,-2) and (4,-3) whose centre lies on the line 3x + 4y = 7


Homework Equations





The Attempt at a Solution



distance from the centre of the circle to the given points is equal
by distance formula and simplifying,
I got 3x-2y=10

On Solving 3x + 4y= 7 and 3x - 2y= 10
I got the point (3,-1/2) as the centre of the circle.
But answer is something else.
Please help
 
Physics news on Phys.org
I get as a second equation
3x -y=10
 
Damn! such a silly mistake
Thanks mate.
 

Similar threads

Circle and a line dividing the circumference
Replies
48
Views
5K
Equation of Circle Passing Through Given Point and Line with Given Radius
Replies
6
Views
1K
Find the center of a circle given a tangent line & point
Replies
2
Views
3K
Equation of a circle from given conditions
Replies
11
Views
2K
Find the scalar, vector, and parametric equations of a plane
Replies
8
Views
3K
Shortest path to a point that doesn't pass through the given circle
Replies
5
Views
2K
Analytic Geometry Question (equation of a circle)
Replies
5
Views
3K
Find the coordinates of a point C from the given line, point and circle
Replies
8
Views
2K
Solve "Find the Equation of the Line with Gradient 3/4 Passing Through (7,11)
Replies
2
Views
2K
Finding the Center and Radius of a Circle with Complex Numbers and Loci
Replies
6
Views
3K

Hot Threads

Recent Insights

Back
Top