This document is about to find the value of "a" considering the circle equation .

Virtual University Of Pakistan

BS Programme of Mathematics or Science

Sub.Name: Calculus & Analytical(mth101)



Question No: 1:

Consider the equation of a circle x2-2x+y2-4y-4=0.If the line2x-y+a=0is its diameter.
Then find the value of a.

Solution:

Equation of a circle

x2-2x+y2-4y-4=0 ------- (i)

To find the value of “a” , first we find the value of x & y.

By,

General Equation of a circle

(x-x0)2 + (y-y0)2 =r2--------- (1)

Rearrange the equation (i)

x2- 2x + y2- 4y = 4------------- (ii)

Applying the complete square method by adding (1)2& (2)2 on both sides of the above equ (ii)

x2-2x+y2-4y+ (1)2+(2)2=4+(1)2+(2)2

Rearrange the equation

x2-2x+(1)2+y2-2(2)(y)+(2)2=4+(1)2+(2)2

(x-1)2+(y-2)2=4+1+4

(x-1)2+(y-2)2=9

(x-1)2+(y-2)2= (3)2

By taking square root on both sides

√(x-1)2+(y-2)2= √(3)2