Question -
Answer -
Given:
Centre = (-2, 3)
Semi – axis are 3 and 2
(i) Whenmajor axis is parallel to x-axis
Now let us find the equation to the ellipse.
We know that the equation of the ellipse with centre (p, q)is given by
Since major axis is parallel to x – axis
So, a = 3 and b = 2.
a2 = 9
b2 = 4
So the equation of the ellipse can be given as
4(x2 + 4x + 4) + 9(y2 – 6y +9) = 36
4x2 + 16x + 16 + 9y2 – 54y +81 = 36
4x2 + 9y2 + 16x – 54y + 61 =0
∴ The equation of the ellipse is 4x2 +9y2 + 16x – 54y + 61 = 0.
(ii) Whenmajor axis is parallel to y-axis
Now let us find the equation to the ellipse.
We know that the equation of the ellipse with centre (p, q)is given by
Since major axis is parallel to y – axis
So, a = 2 and b = 3.
a2 = 4
b2 = 9
So the equation of the ellipse can be given as
9(x2 + 4x + 4) + 4(y2 – 6y +9) = 36
9x2 + 36x + 36 + 4y2 – 24y +36 = 36
9x2 + 4y2 + 36x – 24y + 36 =0
∴ The equation of the ellipse is 9x2 +4y2 + 36x – 24y + 36 = 0.