True or False:
The line 2x + 3y = 12 touches the ellipse `(x^2)/9 + (y^2)/4 = 2` at the point (3,2).

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

The line y=2t^2 intersects the ellipse x^2/9+y^2/4=1 in real points if :

The line 3x -4y = k will cut the circle x^(2) + y^(2) -4x -8y -5 = 0 at distinct points if

The values of lamda for which the line y=x+ lamda touches the ellipse 9x^(2)+16y^(2)=144 , are

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

Find the area of smaller region bounded by the ellipse x^2/9 + y^2/4 = 1 and straight line x/3 + y/2 = 1 .

Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/4=1 touching the ellipse at point A and B. Q. The orthocenter of the trianlge PAB is

Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/4=1 touching the ellipse at point A and B. Q. The coordinates of A and B are

Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=0 . Find the coordinates of the point of contact.