The straight line `x/4+y/3=1` intersects the ellipse `x^2/16+y^2/9 =1` at two points `A` and `B` such that area of `DeltaPAB` is equal to `3`, the number of such `P's` is/are

The straight line (x)/(4)+(y)/(3)=1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9)=1 at two points A and B such that area of Delta PAB is equal to 3, the number of such P's is/are

The straight line (x)/(4)+(y)/(3)=1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9)=1 at two points A and B there is a point P on this ellipse such that the area of Delta PAB is equal to 6(sqrt(2)-1) . Then the number of such point (P) is/are (A) 4 (B) 1 (C) 2 (D) 3

The straight line (x)/(4)+(y)/(3)=1 intersects the ellipse (x^(2))/(16)+(y^(2))/(9)=1 at two points A and B there is a point P on this ellipse such that the area of Delta PAB is equal to 6(sqrt(2)-1) .Then the number of such point (P) is/are

The line x=2y intersects the ellipse (x^(2))/4+y^(2)=1 at the points P and Q . The equation of the circle with PQ as diameter is

The line y=2t^2 meets the ellipse (x^2)/(9)+(y^2)/(4)=1 in real points if

Lines x+y=1 and 3y=x+3 intersect the ellipse x^(2)+9y^(2)=9 at the points P,Q,R. the area of the triangles PQR is

The line 2x+y=3 intersects the ellipse 4x^(2)+y^(2)=5 at two points. The point of intersection of the tangents to the ellipse at these point is