Question

The focus of an ellipse is (–1, –1) and the corresponding directix is x – y + 3 = 0. If the eccentricity of the ellipse is 1/2, then the coordinates of the centre of the ellipse are 

Solution

Correct option is

 

The equation of the axis of the ellipse is   

     

Solving this equation with x – y + 3 = 0, we obtain that the coordinates of z are    

Since A and A’ divide SZ internally and externally respectively in the ration e : 1 i.e. 1 : 2. So, their coordinates are    

        

As C is the mid point of AA’. So, its coordinates are  

        .

SIMILAR QUESTIONS

Q1

If circumcentre of an equilateral triangle inscribed in  with vertices having eccentric angle α, β, γ respectively is (x1y1) then 

Q2

Locus of the middle points of all chords of , which are at a distance of 2 units from the vertex of parabola y2 = –8axis

Q3

A point on the ellipse  at a distance equal to the mean of lengths of the semi-major and semi-minor axis from the centre, is

Q4

A tangent to the ellipse  is cut by the tangent at the extremities of the major axis at T and T’. The circle on TT’ as diameter passes through the point

Q5

 

If C is the centre and A, B are two points on the conic

4x2 + 9y2 – 8x – 36y + 4 = 0 such that ∠ACB = π/2 then CA–2 +CB–2 is equal to  

Q6

Ellipses which are drawn with the same two perpendicular lines as axes and with the sum of the reciprocals of squares of the lengths of their semi-major axis and semi-minor axis equal to a constant have only.

Q7

The eccentricity of the ellipse with centre at the origin which meets the straight line  on the axis of x and the straight line  on the axis of y and whose axes lie along the axes of  coordinates is

Q8

 

The radius of the circle passing through the foci of the ellipse

9x2 + 16y2 = 144 and having its centre at (0, 3), is 

Q9

An ellipse has OB as a semi-minor axis, FF’ as its foci and the angle FBF’ is a right angle. Then, the eccentricity of the ellipse is

Q10

 

The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through (4, 6) is