A man running round a racecourse notes that the sum of the distance of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path he encloses is

The centre of an ellipse is at (0, 0), major axis is on the y-axis. If the ellipse passes through (3, 2) and (1, 6), then what is its eccentricity ?

The sum of the focal distances of a point on an ellipse is constant and equal to the

What is the equation of the ellipse having foci (±2, 0) and the eccentricity \(\frac{1}{4}?\)

Consider any point P on the ellipse \(\frac{{{{\rm{x}}^2}}}{{25}} + \frac{{{{\rm{y}}^2}}}{9} = 1\) in the first quadrant. Let r and s represent its distance from (4, 0) and (-4, 0) respectively, then (r + s) is equal to

Let P(x, y) be any point on the ellipse 25x ²+ 16y ²= 400. If Q(0, 3) and R(0, -3) are two points, then what is (PQ + PR) equal to?

What is PE + PF equal to ?

Consider the following points :

1. \(\left(\frac{\sqrt{3}}{2}, 0\right)\)

2. \(\left(\frac{\sqrt{3}}{2}, \frac{1}{4}\right)\)

3. \(\left(\frac{\sqrt{3}}{2},-\frac{1}{4}\right)\)

Which of the above points lie on latus rectum of ellipse ?

The equation of an ellipse which has a focus (6, 7), a directix x + y + 2 = 0 and eccentricity \(\frac{1}{{\sqrt 3 }}\), is:

The equation of the tangent at the point (x', y') to the ellipse \(\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1\) is:

The equation \(\frac{{{x^2}}}{{2 - r}} + \frac{{{y^2}}}{{r - 6}} + 1 = 0\) represents an ellipse if

The equation of sphere is x² + y² + z² - x + z - 2 = 0, its radius is