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 a focus of the hyperbola x^2/9 - y^2/16 = 1 and its major and minor axes coincide with the transverse and conjugate axes of the hyperbola and the product of eccentricities of ellipse and hyperbola is 1. Foci of the ellipse are (A) (+- 4, 0) (B) (+-3, 0) (C) (+-5, 0) (D) none of these

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

The equation of the circle touching the coordinate axes the line x+2=0 is

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

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.

Find the equation of a line passing through the point (2,3) and parallel to the line 3x-4y+5=0 .

Find the equations of the line which passes through the point (4,4) and the sum of its intercepts on the axes is 16 .

Find the equations of the line which passes through the point (3,4) and the sum of its intercepts on the axes is 14 .