how to calculate the area of an ellipse

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 -..

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 )/..

Choose an equation for the ellipse shown. => 4 x 2 + y 2 = 4 or x 2 + 2 y 2 = 2 or 2 x 2 + y 2 = 2 or x 2 + 4 y 2 = 4..

Equation X 2 /a 2 +y 2 /b 2 =1, a > b X 2 /a 2 +y 2 /b 2 =1, a < b Centre (0,0) (0,0) Coordinate of centre. (a,0),(-a,0) (0,b),(0,-b) Length major axis 2a 2b Length of minor axis 2b 2a Equation of major axis Y = 0 X = 0 Equation of min..

Let, The mass of the organic compound taken be = W g Increase in the mass of magnesium perchlorate tube = W 1 g Increase in the mass of the KOH tube = W 2 g So, Mass of water formed = W 1 g Mass of carbon dioxide formed = W 2 g ..

Let, The mass of the organic compound be = W g Mass of the precipitate of BaSO 4 = W 1 g From stoichiometry, BaSO 4 = S 1 mol 1 mol 1 molecular mass 1 atomic mass 233 g 32 g Therefore, ..

Let, The mass of silver salt taken for ignition be = W g Mass of silver left behind after ignition = W 1 g We have RCOOAg = Ag1 equivalent 1 equivalent The equivalent mass of silver is 108. Hence, the mass of silver salt that would leave 108 g of residue (equivalent mass of the silver) i..

Let, The mass of the organic compound taken be = W g Volume of air displaced = V 1 mL Atmospheric pressure = P mm of Hg Room temperature, T 1 = t o C = (t + 273)K Aqueous tension at t o C = p mm of Hg Pressure of the dry air, P 1 = (P-p) mm Hg ..