If the straight line y=mx is outside the circle `x^(2)+y^(2)-20y+90=0`, then show that `|m|lt3`.

The line y=mx+2 touches the hyperola 4x^(2)-9y^(2)=36 then m=

Consider the following statementas. I. The intercept made by the circle x^(2)+y^(2)-2x-4y+1=0 on Y- axis is 2sqrt(3) II. The intercept made by the circle x^(2)+y^(2)-4x-2y+6=0 on X-axis is 2sqrt(2) III. The straight line y=2x+1 cuts the circle br x^(2)+y^(2) = 9 at two distinct points Then which one of the following option is correct?

If the line y=mx+asqrt(1+m^2) touches the circle x^2+y^2=a^2 , then the point of contact is

The line y=mx+c intersects the circle x^(2)+y^(2)=r^(2) in two distinct points if

The pole of the straight line 9x+y-28=0 with respect to the circle 2x^(2)+2y^(2)-3x+5y-7=0 is

If the point (2,k ) lies outside the circles x^(2) +y^(2) =13 and x^(2) +y^(2) +x-2y -14=0 then