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The focii of the curve represented by x 3 (cost+ sin t), y=4(cos t-sint) is(A)(0,-+root7)(B) (-+root7,0)(C)(-+3/4root7,0)(D)(0,-+3/4root7)(D) (0,Âą4.7(A) (0,tv7(B) (V7,0(C) |7,0 |
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Answer» we have x/3 = cos(t) + sin(t) and y/4 = cos(t) - sin(t) ii) Squaring them and adding, x²/9 + y²/16 = 1This is of the form x²/b² + y²/a² = 1, with a > b.This ellipse center is (0, 0) and major axis along y-axis. b = 3 and a = 4; eccentricity e = √7/4Parametric form of any point on this is (3cos(t), 4sin(t))hence foci is (+-ae,0)hence (+-3/4√7,0) |
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