Coordinates of the vertices B and C of a triangle ABC are (2,0) and (8,0) respectively. The vertex A is varying in such a way that 4tan.2B.tan.2C=1. Then locus of A is
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If the normal at any point P on the ellipse cuts the major and mirror axes in G and g respectively and C be the centre of the ellipse, then
If the normal at any point P on ellipse a2x2+b2y2=1 meets the auxiliary circle at Q and R such that ∠QOR=90∘ where O is centre of ellipse, then
Let Q=(3,5),R=(7,35). A point P in the XY-plane varies in such a way that perimeter of ΔPQR is 16. Then the maximum area of ΔPQR is
If the normal at one end of the latus rectum of the ellipse a2x2+b2y2=1 passes through one end of the minor axis, then prove that ecentricitty is constant.
An equilateral triangle is inscribed in an ellipse whose equation is x2+4y2=4. If one vertex of the triangle is (0,1) then the length of each side is
The mormal at point P(2,233) on the ellipse 16x2+9y2=1 meets the major axis of the ellipse at Q. If S and S are foci of given ellipe, then the rartio SQ:SQ
The foci of an ellise are S(3,1) and S' (11,5). If the normal at is P is x+2y-15=0, then find the coordinattes of point P.
If the length of the major axis intercepted between the tangent and normal at a point P(acosθ,bsinθ) on the ellipse a2x2+b2y2=1 is equal to the length of semi-major axis, then eccentricity of the ellipse is