A circle of radius 1 unit touches the positive x-axis and the positive y-axis at `Aa n dB` , respectively. A variable line passing through the origin intersects the circle at two points `Da n dE` . If the area of triangle `D E B` is maximum when the slope of the line is `m ,` then find the value of `m^(-2)`

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

A line L passing through the focus of the parabola y^2=4(x-1) intersects the parabola at two distinct points. If m is the slope of the line L , then -1 1 m in R (d) none of these

A variable line through the point P(2,1) meets the axes at Aa n dB . Find the locus of the centroid of triangle O A B (where O is the origin).

A line passing through the origin O(0,0) intersects two concentric circles of radii aa n db at Pa n d Q , If the lines parallel to the X-and Y-axes through Qa n dP , respectively, meet at point R , then find the locus of Rdot

A variable line through point P(2,1) meets the axes at Aa n dB . Find the locus of the circumcenter of triangle O A B (where O is the origin).

The line joining the points (x ,2x)a n d(3,5) makes an obtuse angle with the positive direction of the x-axis. Then find the values of xdot

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a) 2 (b) 2/3 (c) 1/3 (d) 3

The equation of the circle passing through the point of intersection of the circle x^2+y^2=4 and the line 2x+y=1 and having minimum possible radius is

The line 3x+6y=k intersects the curve 2x^2+3y^2=1 at points Aa n dB . The circle on A B as diameter passes through the origin. Then the value of k^2 is__________

A straight line is drawn through P(3,4) to meet the axis of x and y at Aa n dB , respectively. If the rectangle O A C B is completed, then find the locus of Cdot