Find the equation of the circle with centre (0, 2) and radius 2.

Find the equation of the circle with centre (–2, 3) and radius 4.

Find the equation of the circle with centre ( , ) and radius .

Find the equation of the circle with centre (1, 1) and radius √2.

Find the equation of the circle with centre (–a, –b) and radius √ (a² − b²).

Find the centre and radius of the circle (x + 5)² + (y – 3)² = 36

Find the centre and radius of the circle x² + y² – 4x – 8y – 45 = 0

Find the centre and radius of the circle x² + y² – 8x + 10y – 12 = 0

Find the centre and radius of the circle 2x² + 2y² – x = 0

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).

Find the equation of the circle passing through (0, 0) and making intercepts a and b on the coordinate axes.

 

Find the equation of a circle with centre (2, 2) and passes through the point (4, 5).

Does the point (–2.5, 3.5) lie inside, outside or on the circle x² + y² = 25?

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 12x.

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = 6y.

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = – 8x.

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the

length of the latus rectum for x² = – 16y.

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 10x.

Find the coordinates of the focus, axis of the parabola, the equation of directrix

and the length of the latus rectum for x² = –9y.

Find the equation of the parabola that satisfies the following conditions:

Focus (6, 0); directrix x = –6.

Find the equation of the parabola that satisfies the following conditions: Focus (0, –3); directrix y = 3.

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0).

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0), focus (–2, 0).

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3)

and axis is along x-axis.

Find the equation of the parabola that satisfies the following conditions:

Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis,

the eccentricity and the length of the latus rectum of the ellipse x² + y² = 1.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity

and the length of the latus rectum of the ellipse x² + y² = 1.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis,

the eccentricity and the length of the latus rectum of the ellipse x² + y² = 1.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis,

the eccentricity and the length of the latus rectum of the ellipse x² + y² = 1.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis,

the eccentricity and the length of the latus rectum of the ellipse x² + y² = 1.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis,

the eccentricity and the length of the latus rectum of the ellipse x² + y² = 1.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis,

the eccentricity and the length of the latus rectum of the ellipse 36x² + 4y² = 144.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis,

the eccentricity and the length of the latus rectum of the ellipse 16x² + y² = 16.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis,

the eccentricity and the length of the latus rectum of the ellipse 4x² + 9y² = 36.

Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0).

Find the equation for the ellipse that satisfies the given conditions:

Vertices (0, ±13),             

foci (0, ±5).

Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0).

Find the equation for the ellipse that satisfies the given conditions:

Ends of major axis (±3, 0), ends of minor axis (0, ±2).

Find the equation for the ellipse that satisfies the given conditions:

Ends of major axis (0, ±√5), ends of minor axis (±1, 0)

Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0).

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6).

Find the equation for the ellipse that satisfies the given conditions: foci (±3, 0), a = 4.

Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.

Find the equation for the ellipse that satisfies the given conditions:

Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Find the equation for the ellipse that satisfies the given conditions:

Major axis on the x -axis and passes through the points (4, 3) and (6, 2).

 

Find the coordinates of the foci and the vertices, the eccentricity,

and the length of the latus rectum of the hyperbola x²- y² = 1.

Find the coordinates of the foci and the vertices, the eccentricity, and the length

of the latus rectum of the hyperbola y² - x² = 1.

Find the coordinates of the foci and the vertices, the eccentricity,

and the length of the latus rectum of the hyperbola 9y² - 4x² = 36.

Find the coordinates of the foci and the vertices, the eccentricity,

and the length of the latus rectum of the hyperbola 16x² – 9y² = 576.

Find the coordinates of the foci and the vertices, the eccentricity, and the

length of the latus rectum of the hyperbola 5y² - 9x² = 36.

 

Find the coordinates of the foci and the vertices, the eccentricity, and the length of

the latus rectum of the hyperbola 49y² - 16x² = 784.

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

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

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5).

 

Find the equation of the hyperbola satisfying the give conditions: foci (±5, 0), the transverse axis is of length 8.

Find the equation of the hyperbola satisfying the give conditions: foci (0, ±13), the conjugate axis is of length 24.

Find the equation of the hyperbola satisfying the give conditions: Foci (±3√5, 0), the latus rectum is of length 8.

Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12.

Find the equation of the hyperbola satisfying the give conditions: Vertices (±7, 0), e = .

Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±√10), passing through (2, 3).

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

An arch is in the form of a parabola with its axis vertical.

The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola.

The road way which is horizontal and 100 m long is supported by vertical wires attached to the cable,

the longest wire being 30 m and the shortest being 6 m.

Find the length of a supporting wire attached to the roadway 18 m from the middle.

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 1.5 m from one end.

A rod of length 12 cm 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 area of the triangle formed by the lines joining the vertex of the parabola x² = 12y to the ends of its latus rectum.

A man running a racecourse note that the sum of the distances from the two flag posts form him is always 10 m

and the distance between the flag posts is 8 m. find the equation of the posts traced by the man.

An equilateral triangle is inscribed in the parabola y² = 4 ax, where one vertex is at the vertex of the parabola.

Find the length of the side of the triangle.