Find the general equation of a circle with centre (-3, -4) and radius 3 units.

Find the equation of the circle described on the chord 3x + y + 5 = 0 of the circle x² + y² = 16 as diameter.

Determine whether x + y − 1 = 0 is the equation of a diameter of the circle x² + y² − 6x + 4y + c = 0 for all possible values of c .

Find the general equation of the circle whose diameter is the line segment joining the points (−4, −2)and (1, 1) is x²+y²+5x+3y+6=0

Examine the position of the point (2, 3) with respect to the circle x² + y² − 6x − 8y + 12 = 0.

The line 3x+4y−12 = 0 meets the coordinate axes at A and B. Find the equation of the circle drawn on AB as diameter.

A circle of radius 3 units touches both the axes. Find the equations of all possible circles formed in the general form.

Find the centre and radius of the circle 3x² + (a + 1)y² + 6x − 9y + a + 4 = 0.

If y = 4x + c is a tangent to the circle x² + y² = 9, find c 

Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.

Find the equation of the circle with centre (2, -1) and passing through the point (3, 6) in standard form.

Find the equation of circles that touch both the axes and pass through (-4, -2) in general form.

Find the equation of the circle with centre (2, 3) and passing through the intersection of the lines 3x − 2y − 1 = 0 and 4x + y − 27 = 0.

Obtain the equation of the circle for which (3, 4) and (2, -7) are the ends of a diameter.

A circle of area 9π square units has two of its diameters along the lines x + y = 5 and x−y = 1. Find the equation of the circle.

If y = 2\(\sqrt2\)x + c is a tangent to the circle x² + y² = 16, find the value of c.

Find the equation of the tangent and normal to the circle x²+y²−6x+6y−8 = 0 at (2, 2) .

Find centre and radius of the following circles.
 x²+ (y + 2)² = 0

Find the length of Latus rectum of the parabola y² = 4ax.

Find the equation of the parabola with focus \(\left( -\sqrt { 2 } ,0 \right) \) and directrix x =\(\sqrt { 2 } \).

Find the equation of the parabola whose vertex is (5, -2) and focus(2, -2) 

Find the equation of the parabola with vertex (-1, -2), axis parallel to y-axis and passing through (3, 6)

Find the vertex, focus, directrix, and length of the latus rectum of the parabola x²−4x−5y−1 = 0.

Find the equation of the ellipse with foci (±2, 0), vertices (±3, 0)  

Find the vertices, foci for the hyperbola 9x²−16y² = 144.

The orbit of Halley’s Comet is an ellipse 36.18 astronomical units long and by 9.12 astronomical units wide. Find its eccentricity.

Find the equation of the parabola in each of the cases given below:
end points of latus rectum (4, -8) and(4, 8) 

Find the equation of the hyperbola in each of the cases given below:
passing through (5, −2) and length of the transverse axis along x axis and of length 8 units.

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
 y² = 16x

Identify the type of the conic for the following equations:
(1) 16y² = −4x²+64
(2) x²+y² = −4x−y+4
(3) x²−2y = x+3
(4) 4x²−9y²−16x+18y−29 = 0

Identify the type of conic section for each of the equations.
2x² − y² = 7

Identify the type of conic section for each of the equations.
3x²+3y²−4x+3y+10 = 0

Identify the type of the conic for the following equations:
3x²+2y² = 14

Identify the type of conic section for each of the equations.
x² + y² + x − y = 0

Identify the type of the conic for the following equations :
11x²−25y²−44x+50y−256 = 0

Identify the type of conic section for each of the equations.
y²+4x+3y+4 = 0

Certain telescopes contain both parabolic mirror and a hyperbolic mirror. In the telescope shown in figure the parabola and hyperbola share focus F₁ which is 14m above the vertex of the parabola. The hyperbola’s second focus F₂ is 2m above the parabola’s vertex. The vertex of the hyperbolic mirror is 1m below F₁. Position a coordinate system with the origin at the centre of the hyperbola and with the foci on the y-axis. Then find the equation of the hyperbola.

Find centre and radius of the following circles.
 x² + y²+ 6x − 4y + 4 = 0

Find centre and radius of the following circles.
x²+y²−x+2y−3 = 0

Find centre and radius of the following circles.
2x²+2y²−6x+4y+2 = 0

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
x² = 24y

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y² = −8x

Find the equation of the parabola in each of the cases given below:
focus (4, 0) and directrix x = −4

Find the equation of the parabola in each of the cases given below:
passes through ( 2, -3) and symmetric about y-axis.

Find the equation of the parabola in each of the cases given below:
vertex (1, -2) and focus (4, -2) 

Find the equation of the hyperbola in each of the cases given below:
 foci(±2, 0), eccentricity = \(\frac { 3 }{ 2 } \)

Find the equation of the hyperbola in each of the cases given below:
Centre (2, 1) one of the foci (8, 1) and corresponding directrix x = 4.