For the ellipse `12 x^2+4y^2+24 x-16 y+25=0` centries `(-1,2)` b. lengths of the axes are `sqrt(3)\ a n d\ 1` c. eccentricity `=sqrt(2/3)` d. all of these

For the ellipse 12 x^2+4y^2+24 x-16 y+25=0 a.centre is (-1,2) b. lengths of the axes are sqrt(3)\ a n d\ 1 c. eccentricity =sqrt(2/3) d. all of these

For the ellipse x^2+4y^2=9 a. the eccentricity is 1/2 b. the latus rectum is 3/2 c. a focus is (3sqrt(3),0) d. a directrix is x=-2sqrt(3)

Consider two straight lines, each of which is tangent to both the circle x^2+y^2=1/2 and the parabola y^2=4x . Let these lines intersect at the point Q . Consider the ellipse whose center is at the origin O(0,\ 0) and whose semi-major axis is O Q . If the length of the minor axis of this ellipse is sqrt(2) , then which of the following statement(s) is (are) TRUE? For the ellipse, the eccentricity is 1/(sqrt(2)) and the length of the latus rectum is 1 (b) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2 (c) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(4sqrt(2))(pi-2) (d) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(16)(pi-2)

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

Find the center, foci, the length of the axes, and the eccentricity of the ellipse 2x^2+3y^2-4x-12 y+13=0

Find the center, foci, the length of the axes, and the eccentricity of the ellipse 2x^2+3y^2-4x-12 y+13=0

Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

The ratio of the area of triangle inscribed in ellipse x^2/a^2+y^2/b^2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse. (A) 1/2 (B) sqrt3/2 (C) 1/sqrt2 (D) 1/sqrt3

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)