Question

x+2y=7-------1
x²+y²=10-----2


Pls do it in Elimination Method

Answer 1

x

2

+y

2

−10x−6y+30=0

⇒(x−5)

2

+(y−3)

2

=(2)

2

Centre =(5,3), radius =2

⇒oA=r=2

OB=r=2

from figure,

⇒AC=r=2

⇒BC=r=2

⇒C=(7,1)

Area of OACB=2×2=4

Smallest circle of family s=0 will have AB as diameter.

∴ Centre = mid point of AB=(6,2)

radius =

2

AB

=

2

2

2

=

2

∴ Equation (x−6)

2

+(y−2)

2

=(

2

)

2

⇒x

2

−12x+36+y

2

−4y+4=2

⇒x

2

−12x+y

2

−4y+38=0

Radical axis of family of circles is 4B

equation of AB is

⇒(y−1)=

7−5

8−1

(x−5)

−y−1=x−5

x−y−4=0

I hope it helps you