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.

P is a point on positive x-axis, Q is a point on the positive y-axis and ' O ' is the origin. If the line passing through P\ a n d\ Q is tangent to the curve y=3-x^2 then find the minimum area of the triangle O P Q , is 3 (b) 4 (c) 5 (c) 6

Circle with centre C(1,1) passes through the origin and intersects the x-axis at A and y -axis at B. The area of the part of the circle that lies in the first quadrant is

If the radisu of the circle passing through the origin and touching the line x+y=2 at (1, 1) is r units, then the value of 3sqrt2r is

A line L passing through the focus of the parabola (y-2)^(2)=4(x+1) intersects the two distinct point. If m be the slope of the line I,, then

A circle C is tangent to the x and y axis in the first quadrant at the points P and Q respectively. BC and AD are parallel tangents to the circle with slope –1. If the points A and B are on the y-axis while C and D are on the x-axis and the area of the figure ABCD is 900 . sqrt(2) sq. units then find the radius of the circle.