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.`

The locus of the midpoint of a chord of the circle x^2+y^2=4 which subtends a right angle at the origins is (a) x+y=2 (b) x^2+y^2=1 (c) x^2+y^2=2 (d) x+y=1

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

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 area of the region bounded by the line y = 2x + 5 and the parabola y = x^(2) - 2x

Show that the equation of the pair of lines bisecting the angles between the pair of bisectors of the angles between the pair of lines a x^2+2h x y+b y^2=0 is (a-b)(x^2-y^2)+4h x y=0.

Find the condition if the circle whose equations are x^2+y^2+c^2=2a x and x^2+y^2+c^2-2b y=0 touch one another externally.

Show that the curves 4x=y^(2)and4xy=k cut at right angles if k^(2)=512 .

Find the shortest distance between the line y=x-2 and the parabola y=x^2+3x+2.

Find the shortest distance between the line y=x-2 and the parabola y=x^2+3x+2.