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

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.

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

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

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

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

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 equation of tangent to the circle x² +y² + 2x - 3y - 8 = 0 at (2, 3).

Find the length of the tangent from (2, -3) to the circle x² + y² - 8x - 9y + 12 = 0.

If the line y = 3x + 1, touches the parabola y² = 4ax, find the length of the latus rectum?

Find the eccentricity of the hyperbola with foci on the x-axis if the length of its conjugate axis is \({ \left( \frac { 3 }{ 4 } \right) }^{ th }\) of the length of its tranverse axis.

Find the equation of the hyperbola whose vertices are (0, ±7) and e = \(\frac { 4 }{ 3 } \)