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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

  • Position of a point with respect to Hyperbola is considered one of the most asked concept.

  • 9 Questions around this concept.

Solve by difficulty

QuestionMEDIUM

The foci of a hyperbola coincide with the foci of ellipse \mathrm{\frac{x^2}{25}+\frac{y^2}{9}=1}. If the eccentricity of the hyperbola is 3 , then its equation is

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If the polar of a point w.r.t. \mathrm{\frac{x^2}{a^2}+\frac{y^2}{b^2}=1} touches the hyperbola \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1}, then the locus of the point is:

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The locus of the poles of the chords of the hyperbola \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1}, which subtend a right angle at the centre is:

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Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

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Concepts Covered - 1

Position of a point with respect to Hyperbola

Position of a point with respect to Hyperbola

Let P(x1,y1) be any point in the plane

\\ {\text { (a) } \mathrm{P} \text { lies outside of the hyperbola : } \frac{\mathrm{x_1}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y_1}^{2}}{\mathrm{b}^{2}}-1<0} \\\\ {\text { (b) } \mathrm{P} \text { lies on of the hyperbola\;\quad\quad: } \frac{\mathrm{x_1}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y_1}^{2}}{\mathrm{b}^{2}}-1=0} \\\\ {\text { (c) } \mathrm{P} \text { lies inside of the hyperbola\quad: } \frac{\mathrm{x_1}^{2}}{\mathrm{a}^{2}}-\frac{\mathrm{y_1}^{2}}{\mathrm{b}^{2}}-1>0}

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Position of a point with respect to Hyperbola

Study other Related Concepts

Position of a point with respect to Hyperbola Current Topic

Coordinate Axes
Distance Between Two Points Formula
Section Formula & Conic Sections
Centroid, Incentre and Circumcentre and Orthocentre of a Triangle
Excenters of Triangle
Circumcentre and Orthocentre
Incentre
Area of Triangle in Coordinate Geometry
Locus
Transformations of Axes

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