In the ellipse `x^2/120+y^2/16=1`, show that the area of the triangle formed by : two foci and one end of minor axis is `8sqrt26`.

In the ellipse x^2/120+y^2/16=1 , show that the area of the triangle formed by : two ends of major axis and one end of minor axis is 8sqrt30 .

Find the area of the triangle formed by the following lines and X axis 4x-3y+4=0 and 4x+3y-20=0

Show that the area of the ellipse x^2/a^2+y^2/b^2=1 is always less than 4ab . Also deduce the area formed by the ends of the latus recta.

A point P on the ellipse x^2/25+y^2/9=1 has the eccentric angle pi/8 . The sum of the distances of P from the two foci is

A line L passeds through the points (1,1) and (2,0) and another line L' passes through ((1)/(2), 0) and perpendicular to L. Then the area of the triangle formed by the lines L, L' and Y-axis is

P is any point on the ellipse x^2/144+y^2/36=1 and S ans S' are foci, then the perimeter of triangle SPS' is :

The lines y = 2x + sqrt 76 and 2y + x=8 touch the ellipse (x ^(2))/(16 )+(y ^(2))/(12)=1. If the point of intersection of these two lines lie on a circle, whose centre coincides with the centre of that ellipse, then the equation of that circle is

The line passing through the extremity A of the major exis and extremity B of the minor axis of the ellipse x^2+9y^2=9 meets is auxiliary circle at the point Mdot Then the area of the triangle with vertices at A ,M , and O (the origin) is 31/10 (b) 29/10 (c) 21/10 (d) 27/10

Find the area of the triangle formed by the lines joining the vertex of the parabola x^2= 12y to the ends of its latus rectum