Circles Math

Question

(i) Given that the line y=mx, where m is a positive integer, does not intersect the circle x²+ y² -4mx +3=0, find the value of m.

 

(ii) A line parallel to y=mx is a tangent parallel to the circle mentioned in (i). Find the equation of this line using the value of m found in (i)

 

 

Ans (i) m=1

      (ii) y=x-2+√2 or y=x-2-√2

 

Thank You!

Answer 1

m=1

two tangent lines

are y=x-2 + 2sqr2

and y=x-2 -2sqr2

1st touches the circle in the top left quarter,

2nd touches the circle in the bottom right side