# Ellipse · Mathematics · JEE Advanced

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JEE Advanced 2024 Paper 1 Online
Consider the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$. Let $S(p, q)$ be a point in the first quadrant such that $\frac{p^2}{9}+\frac{q^2}{4}>1$. Two ta...
JEE Advanced 2022 Paper 1 Online
Consider the ellipse $$\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$$$Let$H(\alpha, 0), 0 .tg {border-collapse:collapse;border-spacing:0;} .tg td{border...
JEE Advanced 2018 Paper 1 Offline
Let S be the circle in the XY-plane defined the equation x2 + y2 = 4.Let P be a point on the circle S with both coordinates being positive. Let the ta...
JEE Advanced 2016 Paper 2 Offline
Let $${F_1}\left( {{x_1},0} \right)$$ and $${F_2}\left( {{x_2},0} \right)$$ for $${{x_1} < 0}$$ and $${{x_2} > 0}$$, be the foci of the ellipse ...
JEE Advanced 2016 Paper 2 Offline
Let $${F_1}\left( {{x_1},0} \right)$$ and $${F_2}\left( {{x_2},0} \right)$$ for $${{x_1} < 0}$$ and $${{x_2} > 0}$$, be the foci of the ellipse ...
JEE Advanced 2014 Paper 2 Offline
The common tangents to the circle $${x^2} + {y^2} = 2$$ and the parabola $${y^2} = 8x$$ touch the circle at the points $$P, Q$$ and the parabola at th...
IIT-JEE 2012 Paper 1 Offline
The ellipse $${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ is inscribed in a rectangle $$R$$ whose sides are parallel to the coordinate axes. Ano...
IIT-JEE 2010 Paper 2 Offline
Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the ellipse at points $$A$$ and $$... IIT-JEE 2010 Paper 2 Offline Tangents are drawn from the point$$P(3, 4)$$to the ellipse$${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$touching the ellipse at points$$A$$and$$...
IIT-JEE 2010 Paper 2 Offline
Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the ellipse at points $$A$$ and $$... IIT-JEE 2009 Paper 2 Offline The normal at a point$$P$$on the ellipse$${x^2} + 4{y^2} = 16$$meets the$$x$$- axis$$Q$$. If$$M$$is the mid point of the line segment$$PQ$$, ... IIT-JEE 2009 Paper 1 Offline The line passing through the extremity$$A$$of the major axis and extremity$$B$$of the minor axis of the ellipse$${x^2} + 9{y^2} = 9$$meets its a... IIT-JEE 2009 Paper 1 Offline Match the conics in Column I with the statements/expressions in Column II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:bla... IIT-JEE 2008 Paper 1 Offline Consider the two curves$${C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0$$. Then, IIT-JEE 2005 Screening The minimum area of triangle formed by the tangent to the$${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$and coordinate axes is IIT-JEE 2004 Screening If tangents are drawn to the ellipse$${x^2} + 2{y^2} = 2,$$then the locus of the mid-point of the intercept made by the tangents between the coordin... IIT-JEE 2003 Screening The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse$${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1,$$i... IIT-JEE 1998 The number of values of$$c$$such that the straight line$$y=4x + c$$touches the curve$$\left( {{x^2}/4} \right) + {y^2} = 1$$is IIT-JEE 1998 If$$P=(x, y)$$,$${F_1} = \left( {3,0} \right),\,{F_2} = \left( { - 3,0} \right)$$and$$16{x^2} + 25{y^2} = 400,$$then$$P{F_1} + P{F_2}$$equals IIT-JEE 1995 Screening The radius of the circle passing through the foci of the ellipse$${{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1$$, and having its centre at$$(0, 3)$$... IIT-JEE 1994 The equation$$2{x^2} + 3{y^2} - 8x - 18y + 35 = k$$represents IIT-JEE 1994 Let$$E$$be the ellipse$${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$and$$C$$be the circle$${x^2} + {y^2} = 9$$. Let$$P$$and$$Q$$be the point... ## MCQ (More than One Correct Answer) JEE Advanced 2023 Paper 1 Online Let T_1 and T_2 be two distinct common tangents to the ellipse E: \frac{x^2}{6}+\frac{y^2}{3}=1 and the parabola P: y^2=12 x. Suppose that the... JEE Advanced 2019 Paper 1 Offline Define the collections {E1, E2, E3, ...} of ellipses and {R1, R2, R3.....} of rectangles as follows :$${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1...
JEE Advanced 2018 Paper 2 Offline
Consider two straight lines, each of which is tangent to both the circle x2 + y2 = (1/2) and the parabola y2 = 4x. Let these lines intersect at the po...
JEE Advanced 2015 Paper 2 Offline
Let $${E_1}$$ and $${E_2}$$ be two ellipses whose centres are at the origin. The major axes of $${E_1}$$ and $${E_2}$$ lie along the $$x$$-axis and th...
IIT-JEE 2009 Paper 2 Offline
An ellipse intersects the hyperbola $$2{x^2} - 2{y^2} = 1$$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If t...
IIT-JEE 2009 Paper 1 Offline
In a triangle $$ABC$$ with fixed base $$BC$$, the vertex $$A$$ moves such that $$\cos \,B + \cos \,C = 4{\sin ^2}{A \over 2}.$$\$ If $$a, b$$ and $$c... IIT-JEE 2008 Paper 1 Offline Let$$P\left( {{x_1},{y_1}} \right)$$and$$Q\left( {{x_2},{y_2}} \right),{y_1} < 0,{y_2} < 0,$$be the end points of the latus rectum of the el... IIT-JEE 1999 On the ellipse$$4{x^2} + 9{y^2} = 1,$$the points at which the tangents are parallel to the line$$8x = 9y$$are ## Numerical JEE Advanced 2021 Paper 2 Online Let E be the ellipse$${{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1$$. For any three distinct points P, Q and Q' on E, let M(P, Q) be the mid-point of... JEE Advanced 2017 Paper 1 Offline For how many values of p, the circle x2 + y2 + 2x + 4y$$-$$p = 0 and the coordinate axes have exactly three common points? JEE Advanced 2013 Paper 1 Offline A vertical line passing through the point$$(h,0)$$intersects the ellipse$${{{x^2}} \over 4} + {{{y^2}} \over 3} = 1$$at the points$$P$$and$$Q$$... ## Subjective IIT-JEE 2005 Find the equation of the common tangent in$${1^{st}}$$quadrant to the circle$${x^2} + {y^2} = 16$$and the ellipse$${{{x^2}} \over {25}} + {{{y^2}...
IIT-JEE 2002
Prove that, in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet...
IIT-JEE 2001
Let $$P$$ be a point on the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,0 < b < a$$. Let the line parallel to $$y$$-axis pas...
IIT-JEE 2000
Let $$ABC$$ be an equilateral triangle inscribed in the circle $${x^2} + {y^2} = {a^2}$$. Suppose perpendiculars from $$A, B, C$$ to the major axis of...
IIT-JEE 1999
Find the co-ordinates of all the points $$P$$ on the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$, for which the area of the tria...
IIT-JEE 1999
Consider the family of circles $${x^2} + {y^2} = {r^2},\,\,2 < r < 5$$. If in the first quadrant, the common taingent to a circle of this family...
IIT-JEE 1997
A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. Prove that the tangents at P and Q of the ellipse x2 + 2y2 = 6 are at...
IIT-JEE 1995
Let '$$d$$' be the perpendicular distance from the centre of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ to the tangent draw...

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IIT-JEE 1996
An ellipse has eccentricity $${1 \over 2}$$ and one focus at the point $$P\left( {{1 \over 2},1} \right)$$. Its one directrix is the common tangent, n...
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