Let the line `y=mx` and the ellipse `2x^(2)+y^(2)=1` intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co - ordinate axes at `(-(1)/(3sqrt2),0) and (0, beta)`, then `beta` is equal to

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

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

P is the extremity of the latusrectum of ellipse 3x^(2)+4y^(2)=48 in the first quadrant. The eccentric angle of P is

P is the extremity of the latuscrectum of ellipse 3x^(2)+4y^(2)=48 in the first quadrant. The eccentric angle of P is

If the line y=mx meets the lines x+2y-1=0 and 2x-y+3=0 at the same point, then m is equal to

If the line y=mx meets the lines x+2y-1=0 and 2x-y+3=0 at the same point, then m is equal to

If the normal to the ellipse 3x^(2)+4y^(2)=12 at a point P on it is parallel to the line , 2x-y=4 and the tangent to the ellipse at P passes through Q (4,4) then Pq is equal to

If the normal to the ellipse 3x^(2)+4y^(2)=12 at a point P on it is parallel to the line , 2x+y=4 and the tangent to the ellipse at P passes through Q (4,4) then Pq is equal to

If the normal to the ellipse 3x^(2)+4y^(2)=12 at a point P on it is parallel to the line , 2x+y=4 and the tangent to the ellipse at P passes through Q (4,4) then Pq is equal to

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