TS EAMCET 04 May 2019 Shift 1 Solved Paper

The equation of the circle passing through (a,0) and (0,b) and(0,0) is,
x2+y2−ax−by=0
Consider the diagram,
Equation of the tangent at origin is given by,
ax+by‌‌=0
PA‌‌=‌

a2

√a2+b2

This implies,
m=|‌

a2

√a2+b2

|‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I)
And
BQ‌‌=n
‌‌=|‌

b2

√a2+b2

‌‌‌‌‌⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II)|
This implies,
m2+n2=‌

a4+b4

a2+b2

And,
mn=‌

a2b2

a2+b2

Now
m2+n2+2mn‌‌=‌

a4+b4+2a2b2

a2+b2

(m+n)2‌‌=‌

(a2+b2)2

a2+b2

‌‌=a2+b2
So, the diameter of circle is given by.
d‌‌=√a2+b2
‌‌=√(m+n)2
‌‌=m+n