find the area of the ellipse

- An ellipse is the set of points in the plane, the sum of whose distance from two fixed points is a given positive constant that is greater than the distance between the two fixed points. Two fixed points are called foci of the ellipse and the mid point of the line segment join..

- An ellipse can also be defined as the locus of a point that moves in such a way that the sum of its distances from two fixed points (called foci) is constant . Equation of an ellipse in standard form [x 2 /a 2 ]+[y 2 /b 2 ]=1 Let x'ox and yoy' be the co-ordinate axes.Let F(c,o..

Proof : - The equation of tangent at (x1,y1) to( x 2 /a 2 )+(y 2 /b 2 ) = 1is (xx1/a 2 )+(yy1/b 2 )=1 ---------------- 1 If the line lx+my+n=0 --------2 , touches the ellipse at the same point ,then 1 and 2 are identical ,So comparing the coefficients of like terms in 1 and 2. [(x1/a 2 )/..

A circle having its centre ,at the centre of an ellipse and the major axis of an ellipse as its diameter is called an auxiliary circle of the ellipse..

Major axis in verticle form of ellipse will be along y axis and the minor axis will be x axis. To derive at the equation of verticle form of ellipse we need to get the points of directrices and length of latus rectu..

An ellipse is the locus of a point that moves in such a way that the ratio of its distance from a fixed point (called focus) to its distance from a fixed line (called directrix)equals a constant e<..

Eccentric angle - Let P(x1,y1) be any point on an ellipse and let PN be perpendicular to the major axis . Suppose NP is produced to meet the auxiliary circle at Q. Let O be the centre of the ellipse , then angle NOQ is known as the eccentric angle..

Answer - Let the given ellipse be (x 2 /a 2 )+(y 2 /b 2 )=1 Let P(x1,y1) be one end of a diameter of the ellipse .Then another end is (-x1,-y1..

The condition for the line y=mx+c to touch the ellipse (x 2 /a 2 )+(y 2 /b 2 )=1 is that c =±√(a 2 m 2 +b 2 ..

Proof : - In order to obtain the points of intersection of the line y=mx+c with the ellipse (x 2 /a 2 )+(y 2 /b 2 )=1 . We solve the equations simultaneously .SO putting y=mx+c in (x 2 /a 2 )+(y 2 /b 2 )=1. We get [x 2 /a 2 ]+[(mx+c) 2 /b 2 ] = 1 or (a 2 m 2 +b 2 )x 2 +2a 2 cmx+a 2 (c 2 -..