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

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

Solve the following:Show that the line 3x-4y+15=0 is a tangent to the circle x^2+y^2=9 ,Find the point of contact.

Show that the line 7x-3y-1=0 touches the circle x^2+y^2+5x-7y+4=0 at point (1,2)

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

Answer the following:Show that the circles touch each other internally.Find their point of contact and the equation of their common tangent. x^2+y^2+4x-12y+4=0,x^2+y^2-2x-4y+4=0

Answer the following:Show that the circles touch each other internally.Find their point of contact and the equation of their common tangent. x^2+y^2-4x-4y-28=0,x^2+y^2-4x-12=0

Answer the following:Show that the circles touch each other externally.find their point of contact and the equation of their common tangent. x^2+y^2-4x-10y+19=0,x^2+y^2+2x+8y-23=0

Answer the following:Show that the circles touch each other externally.find their point of contact and the equation of their common tangent. x^2+y^2-4x+10y+20=0,x^2+y^2+8x-6y-24=0

The lines y = 2x + sqrt 76 and 2y + x=8 touch the ellipse (x ^(2))/(16 )+(y ^(2))/(12)=1. If the point of intersection of these two lines lie on a circle, whose centre coincides with the centre of that ellipse, then the equation of that circle is