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

Let F_1(x_1,0)" and "F_2(x_2,0) , for x_1 lt 0 " and" x_2 gt 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 the area of the triangle MQR to area of the quadrilateral MF_1NF_2 is :

Let F_(1)(x_(1),0) and F_(2)(x_(2),0) , for x_(1)lt0 and x_(2)gt0 , be the foci of the ellipse (x^(2))/(9)+(y^(2))/(8)=1 . Suppose a parabola having vertex at the orgin and focus at F_(2) intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. The orthocentre of the triangle F_(1)MN is

Let F_(1)(x_(1),0) and F_(2)(x_(2),0) , for x_(1)lt0 and x_(2)gt0 , be the foci of the ellipse (x^(2))/(9)+(y^(2))/(8)=1 . Suppose a parabola having vertex at the orgin 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

The foci of the hyperbola 4x^(2)-9y^(2)-1=0 are