Question

define an ellipse derive equation of an ellipsein the form x^2/a^2+y^2/b^2=1​

Answer 1

Step-by-step explanation:

ellipse: it is the set of all points such that the sum of the distance from two fixed point to curve is always constant.

* considerations

*consider an ellipse which is having 2 foci F1 and F2.

*let (c,0) be the co coordinates of F1

*let (-C,0) be the co coordinates of F2.

* let P be the prbitary point on ellipse

* let x and y be the co coordinates of P.

*teh major axis of ellipse is x axis of 2a

*let a,0 be the co coordinates of A.

* let -a,0 be the co coordinates of B.

* a,b be the coordinates of C

* 0,-b be the coordinates of D.

wkt,

PF1 + PF2= constant

PF1+ PF2= 2a

PF1 = (X-C)^2+(Y-0)^2

PF2 =(X+C)^2 +(Y-0)^2