Example 13 Find the equation of the ellipse, with major axis along the

1.	Example 13 Find the equation of the ellipse, with major axis along the x-passing through the points (4, 3) and (-1,4).
Answer» Since it passes through the points (4,3) and (-1,4) these points will satisfy equation of ellipse 4^2/a^2+ 3^2/b^2= 1 and (-1)^2/a^2+ 4^2/b^2= 1 Take 1/a^2= x and 1/b^2= y. ----------(1) Now the above 2 equations become as- 16x + 9y = 1----------(2) and x + 16y = 1----------------(3) Solving the equations(2) and (3) we will get y= 3/49 and x = 1/49 From (1) we get a^2= 49 and b^2= 49/3 Substituting a^2b^2in equation of ellipse when major axis is along x axis we will get- x^2/49 + 3y^2/49 = 1 Thanks

Example 13 Find the equation of the ellipse, with major axis along the x-passing through the points (4, 3) and (-1,4).

Answer»

Since it passes through the points (4,3) and (-1,4) these points will satisfy equation of ellipse

4^2/a^2+ 3^2/b^2= 1 and (-1)^2/a^2+ 4^2/b^2= 1

Take 1/a^2= x and 1/b^2= y. ----------(1)

Now the above 2 equations become as- 16x + 9y = 1----------(2)

and x + 16y = 1----------------(3)

Solving the equations(2) and (3) we will get y= 3/49 and x = 1/49

From (1) we get a^2= 49 and b^2= 49/3

Substituting a^2b^2in equation of ellipse when major axis is along x axis we will get-

x^2/49 + 3y^2/49 = 1

Thanks