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put this solution on YOUR website!The equation of the ellipse with center (h, k) is given by:
+
= 1
Where the length of the major axis is greater than the minor axis.
Here the centre is given by (8, 7) and
length of the major axis = 2a = 16
lenght of the minor axis = 2b = 4
This implies that a = 8 and b = 2
Hence, substituting these in the above formula, we have:
+
= 1
Simplifying these, we have:
+
= 1
Taking LCM and simplifying this further, we have:
= 64
Simplifying this again, we have:
= 64
= 64
= 0
This is the equation of the ellipse.
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2. Write the equation of an ellipse with center (9, –3), horizontal major axis length 18, and minor axis length 10.
Solution:
The equation of the ellipse with center (h, k) is given by:
+
= 1
Where the length of the major axis is greater than the minor axis.
Here the centre is given by (9, -3) and
length of the major axis = 2a = 18
length of the minor axis = 2b = 10
This implies that a = 9 and b = 5
Hence, substituting these in the above formula, we have:
+
= 1
+
= 1
Taking LCM, we get:
= 2025
= 2025
= 2025
= 0
