UPSC NDA Math Model Paper 9

Given equation of circle:
x2+y2−2x−y−1=0
Comparing to the general equation of a circle
ax2+ay2+2gx+2fy+c=0
a=1,g=−1,f=

−1

2

,c=−1
Coordinates of centre =(−

g

a

,−

f

a

)
⇒C=(−

−1

1

,−

−1 2

1

)
⇒C=(1,

1

2

)
Now given line is 6y=8x−9
⇒8x−6y−9=0
Distance between centre C(1,

−1

2

) from given line is:
D=|

ax1+by1+c

√a2+b2

|
⇒D=|

8×1+(−6)× 1 2 +−9

√82+(−6)2

|
⇒D=|

−4

10

|
⇒D=0.4