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प्रश्न
Find the equation for the ellipse that satisfies the given conditions:
Major axis on the x-axis and passes through the points (4, 3) and (6, 2).
उत्तर
Let the equation of ellipse be `x^2/a^2 + y^2/b^2 = 1`
It goes through the points (4, 3) and (6, 2)
`16/a^2 + 9/b^2 = 1` ...(i)
`36/a^2 + 4/b^2 = 1` ...(ii)
On multiplying equation (i) by 4 and equation (ii) by 9
`64/a^2 + 36/b^2 = 4` ...(iii)
`324/a^2 + 36/b^2` ...(iv)
By subtracting equation (iii) from equation (iv),
`260/a^2 = 5`
or `a^2 = 260/52`
Putting the value of a2 in equation (i),
`16/52 + 9/b^2 = 1`
or `9/b^2 = 1 - 16/52 = 36/52`
`9/b^2 = 36/52`
or `b^2 = (9 xx 52)/36 = 13`
∴ Equation of ellipse, `x^2/52 + y^2/13 = 1`.
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