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.`

If the lines joining the origin to the intersection of the line y=nx+2 and the curve x^2+y^2=1 are at right angles, then the value of n^2 is

Show that the curves x=y^2 and x y=k cut at right angles, if 8k^2=1 .

Show that the curves 2x=y^2 and 2x y=k cut at right angles, if k^2=8 .

Show that the curves 4x=y^2 and 4x y=k cut at right angles, if k^2=512 .

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

The portion of the line ax+by-1=0 intercepted between the lines ax+y+1=0 and x+by=0 subtends a right angle at the origin and the condition in a and b is lambda a+b+b^(2)=0, then find value of lambda

Prove that the curves x=y^(2) and cut at right angles* if cut at right angles* if 8k^(2)=1

Find the equation of the lines joining the origin to the points of intersection of the line x+y=1 with the curve 4x^(2)+4y^(2)+4x-2y-5=0 and show that they are at right angles

Find the area bounded on the right by the line x+y=2, on the left by the parabola y=x^(2) and below by the x-axis.