Question #162060

Draw the ellipse with the equation: 2𝑥 2 + 𝑦 2 + 4𝑥 − 9𝑦 = 7


1
Expert's answer
2021-02-24T12:18:35-0500

first of all, we need to transform the equation to the canonical form

(xx0)2a2+(yy0)2b2=1\boxed{\frac {(x-x_0)^2} {a^2} + \frac{(y-y_0)^2} {b^2} = 1} - x0x_0 and y0y_0 - center coordinates


2x2+4x+y29y=72x^2 + 4x + y^2-9y=7


(2x2+4x+2)+(y29y+20.25)=29.25(2x^2 +4x +2) +(y^2 -9y+20.25) = 29.25


2(x+1)2+(y4.5)2=29.252(x+1)^2+(y-4.5)^2 = 29.25


(x+1)214.625+(y4.5)229.25=1\dfrac{(x+1)^2}{14.625} + \dfrac{(y - 4.5)^2}{29.25} = 1


O(-1; 4.5) - center

a=14.6253.8a = \sqrt{14.625} \thickapprox 3.8 - minor semiaxis

b=29.255.4b = \sqrt{29.25} \thickapprox 5.4 - major semiaxes


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Comments

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09.02.21, 00:36

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08.02.21, 14:20

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