Show that the line `y= x + sqrt(5/6` touches the ellipse `2x^2 + 3y^2 = 1`. Find the coordinates of the point of contact.

Show that the line 3x+ sqrt3y =12 is a tangent to the ellipse 9x^(2) +y^(2) = 36 . Find the coordinates of the point of contact.

Show that the straight line x + y=1 touches the hyperbola 2x ^(2) - 3y ^(2)= 6. Also find the coordinates of the point of contact.

Show that the line y =x + sqrt7 touches the hyperbola 9x ^(2) - 16 y ^(2) = 144.

Show that the line x + 2y - 4 = 0 touches the ellipse 3x^(2) + 4y^(2) = 12 also find the point of contact.

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

If the line x + y = 1 touches the parabola y^2-y + x = 0 , then the coordinates of the point of contact are:

Prove that the straight line y = x + a sqrt(2) touches the circle x^(2) + y^(2) - a^(2)=0 Find the point of contact.

If the line y=x+sqrt(3) touches the ellipse (x^(2))/(4)+(y^(2))/(1)=1 then the point of contact is

If x/a+y/b=sqrt2 touches the ellipses x^2/a^2+y^2/b^2=1 , then find the ecentricity angle theta of point of contact.

Show that the line 3x+4y +20=0 touches the circle x^(2) + y^(2) =16 and find the point of contact