Question
Tangents are drawn from the points on a tangent of the hyperbola to the parabola If all the chords of contact pass through a fixed point prove that the locus of the point for different tangents on the hyperbola is an ellipse.
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Practice questions from similar books
Question 1
Find the locus of a point such that the sum of its
distance from the points (2, 2) and
is 6.Question 2
Let be the line passing through the points and . Let be the set of all pairs of circles such that is tangent to at and tangent to at , and also such that and touch each other at a point, say, . Let be the set representing the locus of as the pair varies in . Let the set of all straight lines segments joining a pair of distinct points of and passing through the point be . Let be the set of the mid-points of the line segments in the set . Then, which of the following statement(s) is (are) TRUE?The point lies in (b) The point does NOT lie in (c) The point lies in (d) The point does NOT lie in Stuck on the question or explanation?
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Question Text | Tangents are drawn from the points on a tangent of the hyperbola
to the parabola
If all the chords of contact pass through a fixed point
prove that the locus of the point
for different tangents on the hyperbola is an ellipse. |