Analytic Geometry Answers

If the tangents at two points of a parabola are at right angles, then show that they intersect at a point on the directrix.

Let y^2=4ax be a parabola and p be a point on it. Let the normal at p intersects the x-axis at Q. Draw a line at Q perpendicular to the above normal. Show that the line intersects the parabola y^2+4a(x-2a)=0

If normal at one extremity of latus rectum of an ellipse passes through one extremity of minor axis, prove that the eccentricity e is given by e^4+e^2,-1=0

In a parabola show that the tangent at any point makes equal angles with the foci radius of the point and the line parallel to the x-axis through the point

Given r= -i+2j+2k, find the magnitude of r

The line with equation x+3y=6 cuts the x axis at A the y axis at B .Find the equation of (I) median from origin to AB. (II) median from A to OB. (III) median from B to OA

If

α=3i−j+2k,



β=2i+j−k and

,

γÌ…=i−2j+2k, find


α×β×γ.