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Position of a point with respect to Hyperbola - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
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Position of a point with respect to Hyperbola is considered one of the most asked concept.
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8 Questions around this concept.
Solve by difficulty
Let $a$ and $b$ be the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9 e^2-18 e+5=0$. If $S(5,0)$ is a focus and $5 x=9$ is the corresponding directrix of this hyperbola, then $\mathrm{a}^2-\mathrm{b}^2$ is equal to :
The foci of a hyperbola coincide with the foci of ellipse . If the eccentricity of the hyperbola is 3 , then its equation is
If the polar of a point w.r.t. touches the hyperbola
, then the locus of the point is:
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The locus of the poles of the chords of the hyperbola , which subtend a right angle at the centre is:
Concepts Covered - 1
Position of a point with respect to Hyperbola
Position of a point concerning Hyperbola
Let P(x1,y1) be any point in the plane
(a) P lies outside of the hyperbola : $\frac{\mathrm{x}_1{ }^2}{\mathrm{a}^2}-\frac{\mathrm{y}_1{ }^2}{\mathrm{~b}^2}-1<0$
(b) P lies on of the hyperbola $\quad: \frac{\mathrm{x}_1{ }^2}{\mathrm{a}^2}-\frac{\mathrm{y}_1{ }^2}{\mathrm{~b}^2}-1=0$
(c) P lies inside of the hyperbola : $\frac{\mathrm{x}_1{ }^2}{\mathrm{a}^2}-\frac{\mathrm{y}_1{ }^2}{\mathrm{~b}^2}-1>0$
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