Hyperbola · Mathematics · JEE Advanced

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Numerical

JEE Advanced 2022 Paper 2 Online
Consider the hyperbola $$\frac{x^{2}}{100}-\frac{y^{2}}{64}=1$$ with foci at $S$ and $S_{1}$, where $S$ lies on the positive $x$-axis. Let $P$ be ...
IIT-JEE 2010 Paper 1 Offline
The line $$2x + y = 1$$ is tangent to the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If this line passes through the point o...

MCQ (More than One Correct Answer)

JEE Advanced 2020 Paper 2 Offline
Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola $${{{x^2}} \ov... JEE Advanced 2018 Paper 2 Offline Let T be the line passing through the points P($$-$$2, 7) and Q(2,$$-$$5). Let F1 be the set of al pairs of circles (S1, S2) such that T is tangent t... JEE Advanced 2017 Paper 1 Offline If$$2x - y + 1 = 0$$is a tangent to the hyperbola$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {16}} = 1$$then which of the following CANNOT be sides... JEE Advanced 2015 Paper 2 Offline Consider the hyperbola$$H:{x^2} - {y^2} = 1$$and a circle$$S$$with center$$N\left( {{x_2},0} \right)$$. Suppose that$$H$$and$$S$$touch each o... IIT-JEE 2012 Paper 1 Offline Tangents are drawn to the hyperbola$${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1,$$parallel to the straight line$$2x - y = 1,$$The points of contact... IIT-JEE 2011 Paper 1 Offline Let the eccentricity of the hyperbola$${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$be reciprocal to that of the ellipse$${x^2} + 4{y^2} ...
IIT-JEE 2006
Let a hyperbola passes through the focus of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$$. The transverse and conjugate axes of this...

JEE Advanced 2018 Paper 2 Offline
Let $$H:{{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$, where a > b > 0, be a hyperbola in the XY-plane whose conjugate axis LM subtend...
JEE Advanced 2017 Paper 1 Offline
For $$a = \sqrt 2$$, if a tangent is drawn to a suitable conic (Column 1) at the point of contact ($$-$$1, 1), then which of the following options is...
JEE Advanced 2017 Paper 1 Offline
The tangent to a suitable conic (Column 1) at $$\left( {\sqrt 3 ,\,{1 \over 2}} \right)$$ is found to be $$\sqrt 3 x + 2y = 4$$, then which of the fol...
IIT-JEE 2011 Paper 2 Offline
Let $$P(6, 3)$$ be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at the point $$P$$ intersects the...
IIT-JEE 2010 Paper 1 Offline
The circle $${x^2} + {y^2} - 8x = 0$$ and hyperbola $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ intersect at the points $$A$$ and $$B$$. Equation of...
IIT-JEE 2010 Paper 1 Offline
The circle $${x^2} + {y^2} - 8x = 0$$ and hyperbola $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ intersect at the points $$A$$ and $$B$$. Equation of...
IIT-JEE 2008 Paper 2 Offline
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