Find the equation of the parabola which is symmetric about the Y-axis and psses through the point (2,-3).

If the parabola y² = 4ax passes through the point (3,2), find the length of its latusrectum.

Find the equation of ellipse, if foci are \((\pm 5,0)\) and a=6.

Find the equation of the ellipse, whose axes along coordinates axes, passing through (4,3) and (-1,4).

If the distance between the foci of a hyperbola is 16 and its eccentricity is \(\sqrt { 2 } \) , then find the equation of the hyperbola.

Find the equation of circle whose center is(1, 2) and touches X-axis

Prove that the line lx + my + n=0 will touch the parabola y² = 4ax, if ln = am²

Prove that the radius of the circles x²+ y² = 1, x² + y² - 2x - 6y = 6 and x² + y² - 4x - 12y = 9 are in AP

Find the equation of the circle with
center=(-a,-b) and radius= \(\sqrt { { a }^{ 2 }-{ b }^{ 2 } } \)

Find the equation of the hyperbola with vertices at (0, \(\pm \)6) and e = \(\frac { 5 }{ 3 } \) Find its foci.

Find the equation of the ellipse whose focus is(1,-1), the directrix is the line x-y-3=0 and eccentricity is 1/2.

Find the eccentricity of the hyperbola \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) , when passes through the points (3,0) and \((3\sqrt { 2 } ,2)\)

Draw the shape of the ellipse \(\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 16 } =1\) and find their major axis, minor axis, value of c, vertices, direction, foci, eccentricity and length of latusrectum.

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

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.