Question -
Answer -
Given:
Focus = (1, -2)
Directrix = 3x – 2y + 5 = 0
Eccentricity = ½
Let P(x, y) be any point on the ellipse.
We know that distance between the points (x1, y1)and (x2, y2) is given as
We also know that the perpendicular distance from the point(x1, y1) to the line ax + by + c = 0 is given as
So,
SP = ePM
SP2 = e2PM2
Upon cross multiplying, we get
52x2 + 52y2 – 104x + 208y +260 = 9x2 + 4y2 – 12xy – 20y + 30x + 25
43x2 + 48y2 + 12xy – 134x +228y + 235 = 0
∴ The equation of the ellipse is 43x2 +48y2 + 12xy – 134x + 228y + 235 = 0