Question

Find the equation of the ellipse whose major axis x axis and passes through point (4,3) ,(6,2)

Answer 1

Answer:

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Step-by-step explanation:

The equation of ellipse is

(x^2/a^2)+(y^2+b^2)=1

Substitute (4,3) in the above equation

(16/a^2)+(9/b^2)=1

16b^2+9a^2=a^2b^2....(1)

Subsitute (6,2) in the equation

(36/a^2)+(4/b^2)=1

36b^2+4a^2=a^2b^2...(2)

solving (1) and (2),multiply (1) with 4 and (2) with 9

64b^2+36a^2=4a^2b^2

324b^2+36a^2=9a^2b^2

260b^2=5a^2b^2

a^2=260/5

a^2=52

Substitue in (2)

36b^2+208=52b^2

208=16b^2

b^2=13

Now the equation of the line passing through the points is

x^2/52+y^2/13=1