Answer :

Given that we need to find the equation of the circle passing through the points (5,7), (8,1) and (1,3).



We know that the standard form of the equation of a circle is given by:


x2 + y2 + 2ax + 2by + c = 0 ..... (1)


Substituting (5,7) in (1), we get


52 + 72 + 2a(5) + 2b(7) + c = 0


25 + 49 + 10a + 14b + c = 0


10a + 14b + c + 74 = 0 ..... (2)


Substituting (8,1) in (1), we get


82 + 12 + 2a(8) + 2b(1) + c = 0


64 + 1 + 16a + 2b + c = 0


16a + 2b + c + 65 = 0 ..... (3)


Substituting (1,3) in (1), we get


12 + 32 + 2a(1) + 2b(3) + c = 0


1 + 9 + 2a + 6b + c = 0


2a + 6b + c + 10 = 0 ..... (4)


Solving (2), (3), (4) we get


.


Substituting these values in (1), we get




3x2 + 3y2 - 29x - 19y + 56 = 0


The equation of the circle is 3x2 + 3y2 - 29x - 19y + 56 = 0.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

The equation of tRD Sharma - Mathematics

Find the eqRD Sharma - Mathematics

Find the eqRD Sharma - Mathematics

Show that tRD Sharma - Mathematics

If the circle x<sRD Sharma - Mathematics

Find the eqRD Sharma - Mathematics

Find the eqRD Sharma - Mathematics

The circle xRD Sharma - Mathematics

If the circles x<RD Sharma - Mathematics

If the centroid oRD Sharma - Mathematics