A point P
moves such that the chord of contact of the pair of tangents from P
on the parabola y2=4ax
touches the rectangular hyperbola x2−y2=c2˙
Show that the locus of P
is the ellipse c2x2+(2a)2y2=1.
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Find the equation to which the equation
is transformed if the origin is shifted to the point (2,−3),
the axes remaining parallel to the original axies.
Given that A(1,1)
are two points and D
is a point on AB
produced such that AD=3AB˙
Find the coordinates of D˙
Find the equation of the circle with centre : (1, 1) and radius 2
If three points are A(−2,1)B(2,3),andC(−2,−4)
, then find the angle between ABandBC˙
Find the equation of the parabola that satisfies the given conditions:Vertex (0, 0); focus (3,0)
Find the equation for the ellipse that satisfies the given conditions:Ends of major axis (0,±5), ends of minor axis (±1,0)
Find the area of the pentagon whose vertices are A(1,1),B(7,21),C(7,−3),D(12,2),
An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?