The number of straight lines that can be drawn through the point (-3,4) which are at a distance of 5 units from the point (2,-8) is

Step-by-step solution

Clearly, by figure, line x=-3 is 5 units apart from point Q(2,-8) . Now let ' m ' be the slope of a line passing through (-3,4) and 5 units apart from point Q(2,-8) . Hence equation of line can be given as (y-4)=m(x+3) m x-y+(3 m+4)=0 Since equation (i) is 5 unit apart from Q(2,-8) Hence aligned & m(2)-(-8)+(3 m+4) m^2+(-1)^2 =5 & 5 m+12=5 m^2+1 & 25 m^2+144+120 m=25 m^2+25 & m=- 119 120 aligned Hence (- 119 120 ) x-y+ ( 123 120 )=0 will be 2^ nd equation from (-3,4) which is 5 units apart from (2,-8)