An ellipse passing through the origin has its foci (3, 4) and (6, 8). The length of its semi-minor axis is `bdot` Then the value of `b/(sqrt(2))` is____

Column I, Column II An ellipse passing through the origin has its foci (3, 4) and (6,8). Then the length of its minor axis is, p. 8 If P Q is a focal chord of the ellipse (x^2)/(25)+(y^2)/(16)=1 which passes through S-=(3,0) and P S=2, then the length of chord P Q is, q. 10sqrt(2) If the line y=x+K touches the ellipse 9x^2+16 y^2=144 , then the difference of values of K is, r. 10 The sum of distances of a point on the ellipse (x^2)/9+(y^2)/(16)=1 from the foci is, s. 12

If a line passing through the origin touches the circle (x-4)^2+(y+5)^2=25 , then find its slope.

Consider the ellipse E_1, x^2/a^2+y^2/b^2=1,(a>b) . An ellipse E_2 passes through the extremities of the major axis of E_1 and has its foci at the ends of its minor axis.Consider the following property:Sum of focal distances of any point on an ellipse is equal to its major axis. Equation of E_2 is

in an ellipse with centre at the origin , if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at (0,5,sqrt(3)) , then length of its latus rectum is

For the ellipse x^(2)+ 3y^(2) = a^(2) find the length of major and minor axis.

The parabola y^(2)=4ax passes through the point (2,-6), the the length of its latus rectum is . . . .

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is 1/2, then find the locus of the focus.

An ellipse is sliding along the coordinate axes. If the foci of the ellipse are (1, 1) and (3, 3), then the area of the director circle of the ellipse (in square units) is (a) 2pi (b) 4pi (c) 6pi (d) 8pi

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)

An ellipse passes through the point (2,3) and its axes along the coordinate axes, 3x +2y -1 = 0 is a tangent to the ellipse, then the equation of the ellipse is