An ellipse passes through the point `(4,-1)` and touches the line `x+4y-10=0` . Find its equation if its axes coincide with the coordinate axes.

An ellipse passes through the point (2,3) and its axes along the coordinate axes, 3x +2y -1 = 0 is a tangent to the ellipse, then the equation of the ellipse is

If a circle whose center is (1,-3) touches the line 3x-4y-5=0 , then find its radius.

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

If the foci of an ellipse are (0,+-1) and the minor axis is of unit length, then find the equation of the ellipse. The axes of ellipse are the coordinate axes.

If a line passing through the origin touches the circle (x-4)^2+(y+5)^2=25 , then find its slope.

If a circle passes through the points where the lines 3kx- 2y-1 = 0 and 4x-3y + 2 = 0 meet the coordinate axes then k=

If a hyperbola passing through the origin has 3x-4y-1=0 and 4x-3y-6=0 as its asymptotes, then find the equation of its transvers and conjugate axes.

If a hyperbola passing through the origin has 3x-4y-1=0 and 4x-3y-6=0 as its asymptotes, then find the equation of its transvers and conjugate axes.