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

An ellipse passes through the points (-3,1)&(2,-2)& its principal axis are along the coordinate axes in order.Find its equation.

A straight line passes through the point (2,3) and is suchthat the sum of its intercepts on the co-ordinate axes is 10. Find the equation of the straight line.

Find the equation of a line which passes through the point (3,1) and bisects the portion of the line 3x+4y=12 intercepted between coordinate axes.

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.

Find the equation of the circle passing through the point (-2,1) and touching the line 3x-2y-6=0 at the point (4,3).