Coordinate 82580

Write the equation of the ellipse that passes through the points, and its axes are identical to the coordinate axes when A = [2, 3] and B = [−1, −4].

Correct answer:

e : (x/2.8031)^2+(y/4.2817)^2=1

Step-by-step explanation:

A=(2,3) B=(1,4)  S=(0,0) axSx2+bySy2=1  aAx2+bAy2=1 aBx2+bBy2=1  1/a2 = k 1/b2 = q  Ax2 k + Ay2 q=1 Bx2 k + By2 q=1  22 k+32 q=1 (1)2 k+(4)2 q=1  4k+9q=1 k+16q=1  Row241 Row1Row2 4k+9q=1 13.75q=0.75  q=13.750.75=0.05454545 k=419q=419 0.05454545=0.12727273  k=5570.127273 q=5530.054545  a=1/k=1/0.12732.8031  b=1/q=1/0.05454.2817  e:(x/2.8031)2+(y/4.2817)2=1



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