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=mx to cut at right angles the conic ax^(2)+2hxy+by^(2)=1

Find the condition for the line y= mx to cut at right angles the conic ax^(2)+2hxy+by^(2)=1.

Find the points in which the line y = 2x + 1 cuts the circle x^(2) + y^(2) = 2 .

Find the condition for the lines joining the origin to the points of intersections of 5(x^(2)+y^(2)+bx+ay)=9 ab and (x)/(a)+(y)/(b)=1 are at right angles.

Find the value of m, for which the line y=mx + 25sqrt3/3 is a normal to the conic x^2 /16 - y^2 / 9 =1 .

Find the condition for the line x cos alpha +y sin alpha =p to be a tangent to the ellipse x^2/a^2+y^2/b^2=1 .

Find the condition for the line x cos alpha + y sin alpha = p to be tangent to the hyperbole (x^(2))/(a^(2))-(y^(2))/(b^(2))=1

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

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