Question

20.Major axis on the x-axis and passes through the points (4,3) and (6,2).

Answer 1

It is given that the center is at ( 0,0 ) , major axis is on the x axis and the ellipse passes through (4,3) and ( 6,2 ) .

Since the x axis is the major axis, the equation of the ellipse is represented as x 2 a 2 + y 2 b 2 =1 , where x is the major axis.(1)

( 4,3 ) and ( 6,2 ) lie on the ellipse and satisfy the equation ( 1 )

Substitute ( 4,3 ) in equation ( 1 )

4 2 a 2 + 3 2 b 2 =1 (2)

Substitute ( 6,2 ) in equation ( 1 )

6 2 a 2 + 2 2 b 2 =1 (3)

Multiply equation (3) by 9 4 .

9 4 ( 36 a 2 + 4 b 2 =1 ) 81 a 2 + 9 b 2 =1

Subtract equation (2) from above equation.

16−81 a 2 =− 5 4 65×4 5 = a 2 a 2 =52

Substitute a 2 =52 in (2) to determine b 2 .

16 52 =1− 9 b 2 9 b 2 =1− 4 13 b 2 = 13×9 9

Hence, b 2 =13

Substituting the values of a 2 and b 2 in equation (1), we get

x 2 52 + y 2 13 =1 .

Thus, the equation of the ellipse with the center at ( 0,0 ) , major axis on the x axis and the ellipse passing through (4,3) and ( 6,2 ) is x 2 52 + y 2 13 =1 .