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Ellipse - Defination
Ex 10.3, 1
Ex 10.3, 3
Ex 10.3, 5 Important
Ex 10.3, 2 Important
Ex 10.3, 4
Ex 10.3, 6
Ex 10.3, 9
Example 10 Important
Ex 10.3, 8
Ex 10.3, 7 Important
Ex 10.3, 10
Example, 11
Ex 10.3, 12 Important
Ex 10.3, 11 Important
Ex 10.3, 13
Ex 10.3, 14 Important
Ex 10.3, 15
Example 12 Important
Ex 10.3, 16 Important
Ex 10.3, 17
Ex 10.3, 18 Important
Example 13 Important
Ex 10.3, 19 Important You are here
Ex 10.3, 20
Last updated at May 29, 2023 by Teachoo
Ex 10.3, 19 Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6). Since major axis is along y-axis & centre is at (0,0) So required equation of ellipse is 𝒙^𝟐/𝒃^𝟐 + 𝒚^𝟐/𝒂^𝟐 = 1 Given that ellipse passes through point (3, 2) & (1, 6) Points (3, 2) & (1, 6) will satisfy equation of ellipse. Putting x = 3 & y = 2 in (1) (3)^2/𝑏^2 + (2)^2/𝑎^2 = 1 9/𝑏^2 + 4/𝑎^2 = 1 Putting x = 1 & y = 6 in (1) 〖(1)〗^2/𝑏^2 + 〖(6)〗^2/𝑎^2 = 1 1/𝑏^2 + 36/𝑎^2 = 1 From (3) 1/𝑏^2 + 36/𝑎^2 = 1 1/𝑏^2 = 1 − 36/𝑎^2 Putting value of b2 in (2) 9/𝑏^2 + 4/𝑎^2 = 1 9(1/𝑏^2 ) + 4/𝑎^2 = 1 9(1−36/𝑎^2 ) + 4/𝑎^2 = 1 9 − 324/𝑎^2 + 4/𝑎^2 = 1 (−320)/𝑎^2 = 1 − 9 (−320)/𝑎^2 = −8 1/𝑎^2 = (−8)/(−320) 1/𝑎^2 = 8/320 1/𝑎^2 = 1/40 a2 = 40 Putting value of 𝑎^2 in (3) 1/𝑏^2 + 36/𝑎^2 = 1 1/𝑏^2 = 1 − 36/𝑎^2 1/𝑏^2 = 1 − 36 (1/40) 1/𝑏^2 = (40 − 36)/40 1/𝑏^2 = 4/40 1/𝑏^2 = 1/10 b2 = 10 Now required equation of ellipse is 𝑥^2/𝑏^2 + 𝑦^2/𝑎^2 = 1 Putting value of b2 & a2 𝒙^𝟐/𝟏𝟎 + 𝒚^𝟐/𝟒𝟎 = 1