formula for area of 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 point..

Equation of ellipse is given by (x - h) 2 / a 2 + (y - k) 2 / b 2 = 1 . Where h, k a and b are real number..

If the Point of contacts on the ellipse ,when the lines or the circles in touch with the ellipse ,we call it as parametric representation of ellipse..

Equation of tangent and normal to an ellipse is important with respect to the angle that is made by the lines inside the ellipse as we have seen in auxiliary angl..

What is the center of the ellipse shown? => (0, 0) or (0, 1) or (0, 3) or (- 3, 0)..

General Equation of ellipse is derived with the points of locus F (p,q) and the equation of directrix ax+by+c = 0 along with eccentricity ..

- In this case the major and minor axis of the ellipse along y-axis and x-axis respectively . AA’ =2b and BB’=2a .The foci F and F’ are (0,be)respectively . The directrices DZ and DZ are given by y=b/e and y= -b/e respectively.Length of latus rectum 2b 2 /a The equation ..

Proof - Let QPN be perpendicular to the major axis and O be the centre of the ellipse. Let NOQ=Φ,Then X = ON=OQcosΦ = acosΦ.Since p(x,y) lies on the ellipse (x 2 /a 2 )+(y 2 /b 2 ) = 1 and since x=acosΦ we have[( a 2 cos 2 Φ/a 2 )/a 2 ]+[y 2 /b 2 ]=1 or y 2 /..

- Let e be the eccentricity of an ellipse whose focus is F(p,q) and the equation of whose directrix is ax+by+c=0 Let P(x,y) be a point on the ellipse and PM be the perpendicular on directrix .Then by definition of ellipse PF/PM = e PF 2 = e 2 PM 2 (x-p) 2 + (y-q) 2 = e..

The tangent y=mx+√(a 2 m 2 +h 2 ) touches the ellipse (x 2 /a 2 )+(y 2 /b 2 )=1 at the point [(-a 2 m/√(a 2 m 2 +b 2 ) , b 2 /√(a 2 m 2 +b 2 ..