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.

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

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

Find the equation of the parabola with vertex at the origin, passing through (2, -3) and symmetric about x-axis

If a parabolic reflector is 24 cm in diameter and 6 cm deep, find its locus.

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

Find the locus of a point which divides so that the sum of its distances from (-4, 0) and (4, 0) is 10 units.

For the ellipse x² + 3y² = a², find the length of major and minor axis.

Find the eccentricity of the ellipse with foci on x-axis if its latus rectum be equal to one half of its major axis.

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 = \(\frac { 4 }{ 3 } \)