Q. 55.0( 4 Votes )

Find the equation

Answer :

Given that we need to find the equation of the circle passing through the origin and the points where the line 3x + 4y = 12 meets the axes of co - ordinates.



Let us first find the points at which the line meets the axes.


The value of x is 0 on meeting the y - axis. So,


3(0) + 4y = 12


4y = 12


y = 3


The point is A(0,3)


The value of y is 0 on meeting the x - axis. So,


3x + 4(0) = 12


3x = 12


x = 4


The point is B(4,0)


We have the circle passing through the points O(0,0), A(0,3) and B(4,0).


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


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


Substituting O(0,0) in (1), we get,


02 + 02 + 2a(0) + 2b(0) + c = 0


c = 0 ..... (2)


Substituting A(0,3) in (1), we get,


02 + 32 + 2a(0) + 2b(3) + c = 0


9 + 6b + c = 0


6b + c + 9 = 0 ..... (3)


Substituting B(4,0) in (1), we get,


42 + 02 + 2a(4) + 2b(0) + c = 0


16 + 8a + c = 0


8a + c + 16 = 0 ..... (4)


On solving (2), (3) and (4) we get,



Substituting these values in (1), we get



x2 + y2 - 4x - 3y = 0


The equation of the circle is x2 + y2 - 4x - 3y = 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