Math, asked by Amaan54872, 4 hours ago

(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. ​

Answers

Answered by Aaaryaa
10

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

Answered by diyakhrz12109
17

\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}

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