Circles are drawn through the point (2, 0) to cut intercept of length 5 units on the x-axis. If their centers lie in the first quadrant, then find their equation.

A circle touches the y axis at (0,2) and its x intercept equal to 3 units, then the equation of the circle is

The equaiton of the lines through the point (2, 3) and making an intercept of length 2 units between the lines y+2x=3 and y+2x=5 are

Tangent drawn from the point P(4,0) to the circle x^2+y^2=8 touches it at the point A in the first quadrant. Find the coordinates of another point B on the circle such that A B=4 .

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is 1/2, then find the locus of the focus.

A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. Then find the radius of the circle.

A variable chord is drawn through the origin to the circle x^2+y^2-2a x=0 . Find the locus of the center of the circle drawn on this chord as diameter.

Find the equation of the line through the point (3, 3) and cutting off intercepts on the axes whose sum is 12.

Find the greatest value of x^2 y^3 , where x and y lie in the first quadrant on the line 3x+4y=5 .

Find the equation of the circle passing through the origin and cutting intercepts of lengths 3 units and 4 unitss from the positive exes.