[" (a) Find the condition that the line "y=mx+c" may "],[" touch the circle "x^(2)+y^(2)+2gx+2fy+c=0." I6"]

Find the conditions that the line (i) y = mx + c may touch the circle x^(2) +y^(2) = a^(2) , (ii) y = mx + c may touch the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .

Find the condition that the straight line cx-by+b^(2)=0 may touch the circle x^(2)+y^(2)=ax+by

Find the coodition that the straight line lx+my+n=0 is a normal to the circle x^(2)+y^(2)+2gx+2fy+c=0

Find the condition that the straight line y = mx + c touches the hyperbola x^(2) - y^(2) = a^(2) .

Find the condition that the straight line y = mx + c touches the hyperbola x^(2) - y^(2) = a^(2) .

Find the condition for the line Ix+my+ n = 0 is a normal to the circle x^2 + y^2 + 2gx + 2fy + c = 0 .

The line ax+by+by+c=0 is normal to the circle x^(2)+y^(2)+2gx+2fy+d=0, if

The condition that the line y = mx+c may be a tangent to the hyperbola x^(2) //a^(2) -y^(2)//b^(2) =1 is

If theline y=x touches the circle x^(2)+y^(2)+2gx+2fy+c=0 at P where OP=6sqrt2 then c=