Ex 11.3, 19 - Chapter 11 Class 11 Conic Sections

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Ex 11.3, 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 + = 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 2 + 2 2 2 = 1 9 2 + 4 2 = 1 Putting x = 1 & y = 6 in (1) (1) 2 2 + (6) 2 2 = 1 1 2 + 36 2 = 1 Now equations are 9 2 + 4 2 = 1 (2) 1 2 + 36 2 = 1 (3) From (3) 1 2 + 36 2 = 1 1 2 = 1 36 2 Putting value of b2 in (2) 9 2 + 4 2 = 1 9 1 2 + 4 2 = 1 9 1 36 2 + 4 2 = 1 9 324 2 + 4 2 = 1 320 2 = 1 9 320 2 = 8 1 2 = 8 320 1 2 = 8 320 1 2 = 1 40 So, a2 = 40 Putting value of 2 in (3) 1 2 + 36 2 = 1 1 2 = 1 36 2 1 2 = 1 36 1 40 1 2 = 40 36 40 1 2 = 4 40 1 2 = 1 10 So, b2 = 10 Now required equation of ellipse is 2 2 + 2 2 = 1 Putting value of b2 & a2 + = 1