Question
A tangent to the hyperbola cuts the ellipse at . Show that the locus of the midpoint of is
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Practice questions from similar books
Question 1
The equation of one of the directrices of a hyperboda is
the corresponding focus is (1, 2) and
. Find the equation of the hyperbola and the coordinates of the center and the second focus.Question 2
An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse. If
are the eccentricities of the ellipse and the hyperbola, respectively, then prove that
.Question Text | A tangent to the hyperbola
cuts the ellipse
at
. Show that the locus of the midpoint of
is |