derive the cartesian equation for an ellipse having a horizontal major axis and an arbitrary cen

Step 1: Start with the general equation of an ellipse with center at the origin and major axis a

Derive the cartesian equation for an ellipse having a...

Transcript

00:01 It is asked to find the equation of ellipse, okay? and the center of that ellipse is at origin.

00:08 Here is the center, okay.

00:11 And the major axis is along x -axis.

00:17 So what we observe? let the coordinates of the focus are c .0 and minus c .0.

00:29 And we know one more thing that if there is any point on the ellipse okay then by the definition what does the definition says that some of the distances should be equals to any constant that is length of major axis okay let us consider that this major axis is having length of two way and minor axes have having length of 2b okay so we can see now this pf1 distance should be square root x minus c square plus y square plus square root x plus c squared plus y square is equal to length of major x x2a okay now from here we can see we get square root x square plus c square minus 2c x plus y square is equal to 2 a minus square root x a square plus c squared plus two cx plus y square make the square on both the sides so we get x square plus y square minus 2 cx plus y is equal to 4a square plus x square plus cx plus y square minus then 4a into root of x square plus c square plus c squared then then you can see plus 2x c plus y square okay after cancellation of similar terms okay and then we remain with 4a square plus 4 cx is equal to 4a square root x square plus c squared plus two cx plus y square okay cancel out the common term that is four and once again make the square so we get x square plus c squared plus two cx plus y square is equal to a raise to the power four plus c squared x square and plus two a square cx okay now x square is there okay and we can observe here this is also subtracted.

03:03 So minus c square x squared plus 2a minus 2 a square x and plus y square.

03:13 Okay...

Question

Derive the Cartesian equation for an ellipse having a horizontal major axis and an arbitrary center point.

Question

Derive the Cartesian equation for an ellipse having a horizontal major axis and an arbitrary center point.

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