Find the circumference and area of the circle x² +y² - 2x + 5y + 7 = 0

Find the value of p so that 3x + 4y - p = 0 is a tangent to the circle x² +y² - 64 = 0.

Find the condition for the line lx + my + n = 0 is tangent to the circle x² + y² = a²

Find the area of th triangle found by the lines Joining the vertex of the parabola x² = -36y to the ends of the latus rectum.

Find the equation of the ellipse whose e = \(\frac34\), foci ony-axis, centre at origin and passing through (6, 4).

Find the equation of the ellipse whose latus rectum is 5 and e = \(\frac { 2 }{ 3 } \)

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