Find the range of values of `m` for which the line `y=m x+2` cuts the circle `x^2+y^2=1` at distinct or coincident points.

Find the range of values of lambda for which the point (lambda,-1) is exterior to both the parabolas y^2=|x|dot

Find the condition for the line y=m x to cut at right angles the conic a x^2+2h x y+b y^2=1.

Find the condition for the line y=m x to cut at right angles the conic a x^2+2h x y+b y^2=1.

Find the value of m for which y=m x+6 is tangent to the hyperbola (x^2)/(100)-(y^2)/(49)=1

Find the value of a for which the lines represented by a x^2+5x y+2y^2=0 are mutually perpendicular.

The sides of a triangle have the combined equation x^2-3y^2-2x y+8y-4=0 . The third side, which is variable, always passes through the point (-5,-1) . Find the range of values of the slope of the third line such that the origin is an interior point of the triangle.

Three concentric circles of which the biggest is x^2+ y^2= 1 , have their radii in A.P If the line y= x+1 cuts all the circles in real and distinct points. The interval in which the common difference of the A.P will lie is:

Find the equation of the circle which touch the line 2x-y=1 at (1,1) and line 2x+y=4

Find the value of a for which the lines 2x+y-1=0 2x+y-1=0 a x+3y-3=0 3x+2y-2=0 are concurrent.