If the equation of the ellipse is `3x^2+2y^2+6x-8y+5=0` , then which of the following is/are true? `e=1/(sqrt(3))` Center is `(-1,2)dot` Foci are `(-1,1)a n d(-1,3)dot` Directrices are `y=2+-sqrt(3)`

If the equation of the ellipse is 3x^(2)+2y^(2)+6x-8y+5=0, then which of the following is/are true? e=(1)/(sqrt(3)) Center is (-1,2). Foci are (-1,1) and (-1,3). Directrices are y=2+-sqrt(3)

The co-ordinates of the foci of the ellipse 3x ^(2) + 4y ^(2) -12 x -8y +4=0, are

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

Equation of the ellipse whose focus is (6,7) directrix is x+y+2=0 and e=(1)/(sqrt(3)) is-

The equation of the tangents to the ellipse 4x^2 + 3y^2 = 5 , which are inclined at 60^0 to the X-axis are : (A) y = x/sqrt(3) +- sqrt(65/12) (B) y = sqrt(3) +- sqrt(65/12) (C) y = sqrt(3)x +- sqrt(12/65) (D) none of these

Which of the following is/are true? There are infinite positive integral values of a for which (13 x-1)^2+(13 y-2)^2=((5x+12 y-1)^2)/a represents an ellipse. The minimum distance of a point (1, 2) from the ellipse 4x^2+9y^2+8x-36 y+4=0 is 1 If from a point P(0,alpha) two normals other than the axes are drawn to the ellipse (x^2)/(25)+(y^2)/(16)=1 then |alpha|<9/4dot If the length of the latus rectum of an ellipse is one-third of its major axis, then its eccentricity is equal to 1sqrt(3)

Show that the equation of the normal to the ellipse (x^(2))/(25)+(y^(2))/(9)=1 at ((5)/(sqrt(2)),(3)/(sqrt(2))) is the line 5x-3y=8sqrt(2)

Which of the following is/are true about the ellipse x^2+4y^2-2x-16 y+13=0? the latus rectum of the ellipse is 1. The distance between the foci of the ellipse is 4sqrt(3)dot The sum of the focal distances of a point P(x , y) on the ellipse is 4. Line y=3 meets the tangents drawn at the vertices of the ellipse at points P and Q . Then P Q subtends a right angle at any of its foci.