Tangent drawn from the point P(4,0)
to the circle x2+y2=8
touches it at the point A
in the first quadrant. Find the coordinates of another point B
on the circle such that AB=4
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internally in the ratio λ1:λ2
externally in the ratio λ1;λ2,
then prove that OA
is the harmonic mean of OP
In any triangle ABC, if the angle bisector of ∠Aand perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC
Orthocenter and circumcenter of a DeltaABC
, respectively. If the coordinates of the vertex A
then find the coordinates of the middle point of BC˙
The equation of curve referred to the new axes, axes retaining their directions, and origin (4,5)
. Find the equation referred to the original axes.
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.x2=6y
Find the locus of the point (t2−t+1,t2+t+1),t∈R˙
Find the equation for the ellipse that satisfies the given conditions:Vertices (±5,0), foci (±4,0)
are two points, then find the ratio in which the food of the perpendicular from (4,1)