Find the center and radius of each of the following circle.
x² + y² + 6x -4y + 4 = 0

3

(a)

Find the equation of the ellipse, Whose foci are (\(\pm\)3,0) and passing through (4,1)

3

(a)

Find the eccentricity of the hyperbola whose length of latusrectum is 8 and conjugate axis is equal to the half of its distance between the foci.

3

(a)

Find the equation of ellipse with center at the origin, major axis on the y-axis and passing through the point (3,2) and (1,6).

3

(a)

Find the equation of the parabola whose focus is (2, 0) and directrix is x = -2.

3

(a)

Find the equation of the hyperbola satisfying the given conditions.
Vertices (±2, 0), foci (±3, 0)

3

(a)

Find the equation of the hyperbola satisfying the given conditions.
Vertices (0, ± 5), foci (0, ± 8)

3

(a)

Find the equation of the hyperbola satisfying the given conditions.
Foci (±3\(\sqrt5\) , 0), the latus rectum is of length 8.

3

(a)

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5m from one end.

3

(a)

Find the equation of the circle whose radius is 5 and which touches the circule x²+y²−2x−4y−20=0 externally at the point (3,7).

3

(a)

Show that equation of the circule which touches the co−ordinates axis and whose center lies on the lines lx + my + n = 0 is \((l+m)({ x }^{ 2 }+y^{ 2 })+2n(l+m)(x+y)+{ n }^{ 2 }=0\)

3

(a)

 

Find the area of an equilateral triangle inscribed in the circule x²+y²+2gx+2fy+c=0.

3

(a)

Find the equation of the elipse whose axis are along the co−ordinate axis,vertices are (0,±10) and eccentricity c = 3/5.

3

(a)

 

The foci of an elipse are (±2,0) and its eccentricity is 1/3.Find the equation of elipse.

3

(a)

Find the equation of the hyperbola,the length of whose latusrectum is 8 and eccentricity is \(\frac { 3 }{ \sqrt { 5 } } \)

3

(a)