Determine the equation of major and minor axes of the ellipse
Also, find its centre, length of the latusrectum and eccentricity.
The equation of the ellipse can be written as
Here a > b
∴ Equation of major axis is Y = 0
Equation of minor axis is X = 0
Centre : X = 0, Y = 0
x = –1, y = 0
∴ Centre is (–1, 0)
Length of latus rectum
If the angle between the straight lines joining foci and the ends of the minor axis of the ellipse is 90o. Find its eccentricity.
Find the equation of the ellipse referred to its centre whose minor axis is equal to the distance between the foci and whose latus rectum is 10.
The extremities of a line segment of length l move in two fixed perpendicular straights lines. Find the locus of that point which divides this line segment in ratio 1 : 2.
Find the lengths and equations of the focal radii drawn from the point on the ellipse 25x2 + 16y2 = 1600.
For what value of λ dose the line y = x + λ touches the ellipse
9x2 + 16y2 = 144.
Find the equations of the tangents to the ellipse which are perpendicular to the line y + 2x = 4.
Find the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse .
Find the locus of the points of the intersection of tangents to ellipse which make an angle θ.
Find the locus of the poles of tangents to with respect to the concentric ellipse .
Find the locus of the centroid of an equilateral triangle inscribed in the ellipse