Geometry

Conic Sections

Conics - Hyperbola

         

Consider a branch of the hyperbola x22y225x42y3=0x^2-2y^2-2\sqrt{5}x-4\sqrt{2}y-3=0 with vertex at a point A.A. Also, let BB be one of the end points of its latus rectum. If CC is the focus of the hyperbola nearest to point A,A, what is the area of triangle ABC?ABC ?

What are the coordinates of the foci of the rectangular hyperbola x2y2=72?x^2-y^2=7 ^2?

What are the coordinates of the vertices of the hyperbola 4x29y240x+54y17=0?4x^2-9y^2-40x+54y -17=0 ?

Given points F=(5,0)F=(5,0) and F=(5,0),F'=(-5,0), what is the equation of the locus of points PP in a plane such that PFPF=8? \left\lvert \left\lvert \overline{PF} \right\rvert - \left\lvert \overline{PF'} \right\rvert \right\rvert= 8 ?

Note: AB\lvert \overline{AB} \rvert denotes the length of line segment AB.\overline{AB}.

Suppose that (7,12)(7,12) and (11,8)(11,8) are the foci of a hyperbola passing through the origin. Then the eccentricity of the hyperbola is _________.\text{\_\_\_\_\_\_\_\_\_}.

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