Question

(a,c) and (b,c) are the centres of two circles whose radical axis is the y-axis. If the radius of first circle is r then the diameter of the other circle is ?

Need Valid Answer..Aur haan !! abhi chahiye. ​

Answer 1

Answer:

Let radius of after circle be R

C

1

:(x−a)

2

+(y−c)

2

=r

2

C

2

:(x−b)

2

+(y−c)

2

=R

2

Radius axis →x=0 OR c

1

−c

2

=0

c

1

−c

2

=x

2bx−2ax−r

2

+R

2

+a

2

−b

2

=x

Put x=0

R

2

=r

2

+b

2

−a

2

R=

r

2

+b

2

−a

2

Diameter =2

r

2

+b

2

−a

2

D is correct

Answer 2

$\huge\bf\star\fbox\red{ᴀɴsᴡᴇʀ:-}$

ʟᴇᴛ ᴛʜᴇ ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴄᴇɴᴛᴇʀ ʙᴇ R

$c1 \: \:( : x \: - \:a \: )^{2} + (y - c)^{2} \: \: = {r}^{2}$

$c2 \: : \: (x - b )^{2} + (y - c )^{2} = {R}^{2}$

ʀᴀᴅɪᴜs ᴀxɪs ☞︎︎︎ x = 0 Oʀ ᴄ1 - ᴄ2 = 0

ᴄ1 - ᴄ2 = x

$2ʙx -2ᴀx - {r}^{2} + {R}^{2} + \: {a}^{2} - {b}^{2} = x$

ᴘᴜᴛ x = 0

R^2 = ʀ^2 + ʙ^2 -ᴀ^2

R^2 =ʀᴏᴏᴛ ᴏғ ʀ^2 + ʙ^2 -ᴀ^2

$ᴅɪᴀᴍᴇᴛᴇʀ \: = 2 \sqrt{r} ^{2} + \sqrt{b} ^{2} - \sqrt{a} ^{2}$