Which is the equation of an ellipse with directrices at y = ±2 and foci at (0, 1) and (0, −1)? x squared over 4 plus y squared over 1 equals 1
x squared over 1 plus y squared over 2 equals 1
x squared over 1 minus y squared over 4 equals 1
x squared over 1 minus y squared over 2 equals 1

b) Equation of the ellipse    

Step-by-step explanation:

Explanation:-

step(i):-

Given the direct rices of the ellipse   y = ±2

Given foci of the ellipse F( 0 ,± c) = ( 0,±1)

The  the direct rices of the ellipse

                                              y = ±    

                                               a = 2 e ...(i)

Given focus ( 0 , c) = ( 0, a e) = ( 0,1)

                                            a e = 1 ...(ii)

From (i) and (ii)

                                   2 e (e) = 1

                                   2 e² = 1

Step(ii):-

                         Now a = 2 e = 2 ()

                                a  = √2

Now we know that The relation between the focus and minor and major axes

formula  C² = a² - b²

                                            b² = a ² - C²

                                             b²  = 2 - 1 = 1

Step(iii):-

Equation of the ellipse

Conclusion:-

Equation of the ellipse    

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