Here is how I solved it. <span>1. The foci are (12, 0) and (-12, 0) </span> <span>--> which means: </span> <span>i) that c=12, </span> <span>ii) the x-axis is the major horizontal axis (because the 12 and -12 are x co-ordinates values) </span> <span>iii) the center of the ellipse is at the origin (0,0) </span> <span>2.The endpoints of the minor axis are at (0,5) and (0,-5), </span> <span>--> from this we know the length of the y-axis is 10, therefore b=5 </span>
<span>Using the formula a² = c² + b² , where c=12, b=5, solve for a. </span> <span>a² = (12)² + (5)² </span> <span>a² = 144 + 25 </span> <span>a² = 169 </span> <span>a = 13 </span>
<span>The standard form of the equation of the ellipse with horizontal major axis is: </span> <span>(x - h)² / a² + (y - k)² / b² = 1, where (h,K)=(0,0) and a²=169, b²=25 </span>
<span>2nd question: The ellipse equation is (x - 2)²/4 + (y - 4)²/64 = 1 </span>
<span>1.The endpoints of the major axis are at (2,12) and (2,-4). </span> <span>--> this means: </span> <span>i) The y-axis is the major vertical axis </span> <span>ii) the length of the major axis is (12+4)=16, therefore a=8, </span> <span>iii) the center is not at the origin (0,0) but half way between -4 and 12. </span> <span>(which is calculated by (-4 + 12)/2 = 4). Therefore the center (h,k) = (2,4) </span>
<span>2. The endpoints of the minor axis (x-axis) are at (4,4) and (0,4) </span> <span>--> from this we know the length of the axis is 4, therefore b=2 </span>
<span>The standard form of the equation of the ellipse with vertical major axis is: </span> <span>(x - h)² / b² + (y - k)² / a² = 1, where a²=64, b²=4, h=2, k=4 </span>