Question

The centre of a circle is (3,1) and it makes an intercept of a 6 units on 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

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