Question -
Answer -
Given:
Major axis on the x-axis and passes through the points (4, 3)and (6, 2).
Since the major axis is on the x-axis, the equation of theellipse will be the form
x2/a2 + y2/b2 =1…. (1) [Where ‘a’ is the semi-major axis.]
The ellipse passes through points (4, 3) and (6, 2).
So by putting the values x = 4 and y = 3 in equation (1), we get,
16/a2 + 9/b2 = 1 …. (2)
Putting, x = 6 and y = 2 in equation (1), we get,
36/a2 + 4/b2 = 1 …. (3)
From equation (2)
16/a2 = 1 – 9/b2
1/a2 = (1/16 (1 – 9/b2)) …. (4)
Substituting the value of 1/a2 in equation (3)we get,
36/a2 + 4/b2 = 1
36(1/a2) + 4/b2 = 1
36[1/16 (1 – 9/b2)] + 4/b2 = 1
36/16 (1 – 9/b2) + 4/b2 = 1
9/4 (1 – 9/b2) + 4/b2 = 1
9/4 – 81/4b2 + 4/b2 = 1
-81/4b2 + 4/b2 = 1 – 9/4
(-81+16)/4b2 = (4-9)/4
-65/4b2 = -5/4
-5/4(13/b2) = -5/4
13/b2 = 1
1/b2 = 1/13
b2 = 13
Now substitute the value of b2 in equation (4)we get,
1/a2 = 1/16(1 – 9/b2)
= 1/16(1 – 9/13)
= 1/16((13-9)/13)
= 1/16(4/13)
= 1/52
a2 = 52
Equation of ellipse is x2/a2 + y2/b2 =1
By substituting the values of a2 and b2 inabove equation we get,
x2/52 + y2/13 = 1