Let `S(x_(1),0)` for `x_(1)>0` is focus of the ellipse `E:(x^(2))/(9)+(y^(2))/(4)=1.` Suppose a parabola whose vertex is `V(x_(1)sqrt(5),0)` touches the ellipse at points `A` and `B` in `I` and `IV` quadrants respectively. Axis of parabola is `x` - axis. Equation of normal to the ellipse `E` at `A` is

Equation of normal to the ellipse at (x_(1);y_(1))

For the ellipse ((x+y-1)^(2))/(9)+((x-y+2)^(2))/(4)=1 the end of major axis are

The coordinates of a focus of the ellipse 4x^(2) + 9y^(2) =1 are

Consider an ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 What is the eauation of parabola whose verted is at (0, 0) and focus is at (0, 2) ?

let A(x_(1),0) and B(x_(2),0) be the foci of the hyperbola (x^(2))/(9)-(y^(2))/(16)=1 suppose parabola having vertex at origin and focus at B intersect the hyperbola at P in first quadrant and at point Q in fourth quadrant.

Let F_1(x_1,0) and F_2(x_2,0), for x_1 0, be the foci of the ellipse x^2/9+y^2/8=1 Suppose a parabola having vertex at the origin and focus at F_2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF_1 NF_2 is