Ellipse. The line passing thru the extremity A of the major axis and extremity B of the minor axis of ellipse x2+9y2=9 meet its auxiliary circle at the point M.then the area of the triangle with vertices at A,M and origin.

Dear Nirbhay,

The Ellipse: Equation of an Ellipse, Eccentricity, Focus, Major and Minor Axis, Chords and Latus Rectum:

• The ellipse is the locus of a point in a plane such that the ratio of distance of that point from a fixed point, focus, to the ratio of the distance of that point from a fixed line, the directrix, is constant and is always less than one.
• The ratio is called eccentricity, denoted by e.
• The equation ax2+2hxy+by2+2gx+2fy+c=0 denotes an ellipse when abc+2fgh-af2-bg2-ch2≠0 and h2-ab<0.
• Every ellipse has two axis, major and minor. The major axis is perpendicular to directrix and passes through the focus.
• Also, there are two ‘focus’ in an ellipse, and hence two ‘directrix’, one corresponding to each. Every point’s distance from each focus to the point’s distance from the corresponding directrix is in a constant ratio e.
• The minor axis is parallel to the directrix and bisects the line joining the two foci. The point where major and minor axis meet is called the center of ellipse.

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