Find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

For the hyperbola 3x² - 6y² = -18, find the length of transverse and conjugate axes and eccentricity.

Find the value of c if y = x + c is a tangent to the hyperbola 9x² - 16y² = 144.

Show that the line x + y + 1 = 0 touches the hyperbola \(\frac { { x }^{ 2 } }{ 16 } -\frac { { y }^{ 2 } }{ 15 } \) = 1 and find the co-ordinates of the point of contact

Find the equation of the circle, which is concentric with the circle \(x^{2}+y^{2}-4 x-6 y-9=0\) and passing through the point (- 4, - 5).

Find the equation of the tangent to \(x^{2}+y^{2}-4 x+4 y-8=0 \text { at }(-2,-2)\)

Find the length of the chord intercepted by the circle \(x^{2}+y^{2}-2 x-y+1=0\) and the line x - 2y = 0

Find the value of p if the line 3x + 4y - p = 0 is a tangent to the circle \(x^{2}+y^{2}=16\)

Write an equation of each circle, given the following information :
a. centre at the origin and radius 7
b. centre at (-1, 3) and radius 4
c. centre at (3, 1) and passing through the point (5, 4)

Find the equations of the tangent, and normal to the parabola \(x^{2}+x-2 y+2=0\) at (1, 2).

Find the point on the parabola y = 12x at which the ordinate is double the abscissa.

Find the equation of the parabola whose co-ordinates of vertex and focus are (- 2, 3) and (1, 3) respectively.

Find the eccentricity, centre, foci, vertices of the following ellipse \(\frac{(x+3)^{2}}{6}+\frac{(y-5)^{2}}{4}=1\).

Find the equation of the ellipse whose one of the foci is (2, 0) and the corresponding directrix is x = 8 and eccentricity \(\frac{1}{2}\)

Find the equation of the ellipse with focus (-1, -3), directrix x-2y = 0 and eccentricity \(\frac{4}{5}\)