Find the equation of the ellipse with foci at \((\pm 5,0)\) and x=\(\frac { 36 }{ 5 } \) as one of the directrices.

Find the eccentricity of the hyperbola, the length of whose conjugate axis is 3/4 of the length of transverse axis.

Find the equation of the circle whose centre is (2,-3) and which passes through the intersection of the lines 3x + 2y + 11 and 2x + 3y = 4

If lx +my = 1 touches the circle x²+y² = a², then prove that the point (l,m) lies on the circle x²+y²=a^-2.

Find the equation of the circle with circle=(2,3) and radius=5

Find the centre and radius of each of the following circles.
\((x-\frac { 1 }{ 2 } { ) }^{ 2 }+(y+\frac { 1 }{ 3 } { ) }^{ 2 }=\frac { 1 }{ 4 } \)

Find the center and radius of each of the following circle
x² + y² -6x + 5y - 8 = 0

Find the equation of circle whose center is(1,2) and which passes through the point(4,6)

If the line y=mx +1 is tangent to the parabola y²=4x, then find the value of m

Draw the shape of \(\frac { { x }^{ 2 } }{ 100 } +\frac { { y }^{ 2 } }{ 400 } =1\)and find their vertices, major axis, minor axis, eccentricity, foci, and length of latusrectum.

Find the equation of the ellipse whose centre is at origin and the X-axis, the major axis, which passes through the points (-3,1) and (2,-2).

Draw the shape of ellipse \(\frac { { x }^{ 2 } }{ 49 } +\frac { { y }^{ 2 } }{ 16 } =1\)and find the vertices.

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4x +y = 16.

Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2,3).

A man running a race leave no space course notes that the sum of the distances from the two flag posts from him is always 10m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.