d Problem: Find the equation of the circle with diameter AB, if A(-3,2) and B(1,4). | Job Exam Rare Mathematics (JEMrare) - Solved MCQs

# Problem: Find the equation of the circle with diameter AB, if A(-3,2) and B(1,4).

Problem: Find the equation of the circle with diameter AB, if A(-3,2) and B(1,4).

Solution:

Before moving to solution we should know that standard equation of a circle with radius ‘r’ and center at point O(a,b) is;

$(x-a)^2+(y-b)^2=r^2$

As it is given that AB is the diameter, so the mid point will be the center of the circle !

So, our first priority is to find the center of the circle !

Mid point of a straight line AB will be ;

$(\frac{-3+2}{2}, \frac{1+4}{2})$

or,

$(-1/2,5/2)$

Now to find radius of the circle we proceed as below;

Diameter AB of the circle by distance formula will be,

$r=\sqrt{(2+3)^2+(4-1)^2}$

$r=\sqrt{34}$

Radius will be half of the diameter, so,

$r= \frac{\sqrt{34}}{2}$

So the equation of circle will be,

$(x+\frac{1}{2})^2+(y-\frac{5}{2})^2=(\frac{\sqrt{34}}{2})^2$

After simplification we will get equation of the circle as;

$x^2+y^2+x-5y-2=0$