Question

Find The equation of The Circle Whose centre is (3,-1) and which cuts off an intercept of 6 from the line 2x - 5y + 18 = 0

Answer 1

Hi

If the circle cuts an intercept of 6 units of that line, that means length of the chord inside the circle is 6 units.

now drop a perpendicular from center to the line, it should bisect the chord.

Length of perpendicular dropped from center can be found out by

 

p=|2*3-5*(-1)+18|/root(2^2+5^2) =root(29)

 

From Pythagoras theorem,

root(p^2+3^2)=r^2, where r is the radius of the circle

=>r=root(38)

 hence, equation of circle is

(x-3)^2 + (y+1)^2 = 38

Hope it helps

Please mark it the brainliest!!

:))

Answer 2

HII #DEAR ♥️♥️♥️♥️♥️♥️

ֆօʟʊȶɨօռ▪▪▪▪▪


ʟᴇɴɢᴛʜ ᴏғ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴅʀᴏᴘᴘᴇᴅ ғʀᴏᴍ ᴄᴇɴᴛᴇʀ ᴄᴀɴ ʙᴇ ғᴏᴜɴᴅ ᴏᴜᴛ ʙʏ   ᴘ=|2×3-5(-1)+18|/ʀᴏᴏᴛ(5^2+2^2) =ʀᴏᴏᴛ(29)  

ғʀᴏᴍ ᴘʏᴛʜᴀɢᴏʀᴀs ᴛʜᴇᴏʀᴇᴍ, ʀᴏᴏᴛ(ᴘ^2+3^2)=ʀ^2,

ᴡʜᴇʀᴇ ʀ ɪs ᴛʜᴇ ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴄɪʀᴄʟᴇ =>

ʀ=ʀᴏᴏᴛ(38)

  ʜᴇɴᴄᴇ,

ᴇǫᴜᴀᴛɪᴏɴ ᴏғ ᴄɪʀᴄʟᴇ ɪs (x-3)^2 + (ʏ+1)^2= 38


HØPE IT HELPS U...!!♥️♥️♥️♥️♥️