Find K, if the line `3x+4y+k=0` touches the ellipse `9x^2+16y^2=144`.

Show that the line x-y=5 is a tangent to the ellipse 9x^2+16y^2=144 . Find the point of contact.

Show that the line 8y+x=17 touches the ellipse x^2+4y^2=17 . Find the point of contact.

The latus rectum of the ellipse 9x^2+16y^2=144 , is:

Find the equations of the tangents to the ellipse x^2/16+y^2/9=1 , making equal intercepts on coordinate axes.

If the line 3x-4y=k touches the hyperbola x^2/5-(4y^2)/5=1 , then find the value of k.

Find the equation of the tangent to the ellipse 5x^(2) + 9y^(2) = 45 which are bot to the line 3x + 2y + 7 = 0.

Find the equation of the tangent to the hyperbola: 9x^2-16y^2=144 at the point L of latus rectum in the first quadrant.