Q17 of 112 Page 166

If x + 2y = 7 and 2x + y = 8 are the equations of the lines of two diameters of a circle, find the radius of the circle if the point (0, –2) lies on the circle.

Given: The equations of the lines of two diameters of a circle


are x + 2y = 7 and 2x + y = 8 and F(0,–2)



Now to find the center of the circle,we have to find the


intersection of the lines x + 2y = 7 and 2x + y = 8


x + 2y = 7–––(1)


2x + y = 8–––(2)


Multiplying (1) by 2,we get




Substitute y = 2 in x + 2y = 7 we get,


x + 2(2) = 7


⇒ x = 7 – 4 = 3


The point of intersection is (3,2) i.e.the center.


Therefore distance between the points (3,2) and (0,–2) is



=


=


=


= 5 units


Hence the radius of the circle is 5 units.


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