Find the condition, that the line lx + my + n = 0 may be a tangent to the circle `(x - h)^(2) + (y - k)^(2) = r^(2)` .

Find the condition that line lx + my - n = 0 will be a normal to the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 .

The condition that the line lx +my+n =0 to be a normal to y^(2)=4ax is

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

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 .

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

If lx + my + n = 0 is tangent to the parabola x^(2)=y , them

Find the value of k so that the line y = 3x + k is a tangent to the parabola y^(2) = - 12 x

If the line lx+my+n=0 is tangent to the circle x^(2)+y^(2)=a^(2) , then find the condition.

Show that the line lx+my+n=0 is a normal to the circles S=0 iff gl+mf=n .

If the chord of contact of the tangents from the point (alpha, beta) to the circle x^(2)+y^(2)=r_(1)^(2) is a tangent to the circle (x-a)^(2)+(y-b)^(2)=r_(2)^(2) , then