Find  the equation of the hyperbola whose one directrix is x + =9, the corresponding focus is (2,2) and eccentricity is 2. 

Find the foci,vertices, eccentricity and length of latusrectum of the hyperbola \(5{ y }^{ 2 }+{ 9x }^{ 2 }=36\)

If a latusrectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse.

Find the equation of the circle passing through the vertices of a triangle whose sides are represented by the equations x+y=2, 3x-4y=6 and x-y=0

The foci of a hyperbola coincide with the faci of the elipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\) find the equation of the hyperbola if its eccentricity is 2.

Find the equation of the hyperbola satisfying the given conditions.
Foci (0, ± \(\sqrt10\) ),passing through (2, 3)

A rod of length 12cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x +y = 16.

Find the equation of the circle passing through the points (2,3) and (-1, 1) and whose centre is on the line x - 3y - 11 =0.

Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2,3).

A man running a race leave no space course notes that the sum of the distances from the two flag posts from him is always 10m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.