# Parabola · Mathematics · JEE Advanced

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## MCQ (More than One Correct Answer)

JEE Advanced 2024 Paper 2 Online
Let $A_1, B_1, C_1$ be three points in the $x y$-plane. Suppose that the lines $A_1 C_1$ and $B_1 C_1$ are tangents to the curve $y^2=8 x$ at $A_1$ an...
JEE Advanced 2022 Paper 1 Online
Consider the parabola $$y^{2}=4 x$$. Let $$S$$ be the focus of the parabola. A pair of tangents drawn to the parabola from the point $$P=(-2,1)$$ meet...
JEE Advanced 2021 Paper 2 Online
Let E denote the parabola y2 = 8x. Let P = ($$-$$2, 4), and let Q and Q' be two distinct points on E such that the lines PQ and PQ' are tangents to E....
JEE Advanced 2017 Paper 1 Offline
If a chord, which is not a tangent, of the parabola y2 = 16x has the equation 2x + y = p, and mid-point (h, k), then which of the following is(are) po...
JEE Advanced 2016 Paper 2 Offline
Let $$P$$ be the point on the parabola $${y^2} = 4x$$ which is at the shortest distance from the center $$S$$ of the circle $${x^2} + {y^2} - 4x - 16y... JEE Advanced 2016 Paper 1 Offline The circle$${C_1}:{x^2} + {y^2} = 3,$$with centre at$$O$$, intersects the parabola$${x^2} = 2y$$at the point$$P$$in the first quadrant, Let the... JEE Advanced 2015 Paper 1 Offline Let$$P$$and$$Q$$be distinct points on the parabola$${y^2} = 2x$$such that a circle with$$PQ$$as diameter passes through the vertex$$O$$of th... IIT-JEE 2011 Paper 2 Offline Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by IIT-JEE 2010 Paper 1 Offline Let$$A$$and$$B$$be two distinct points on the parabola$${y^2} = 4x$$. If the axis of the parabola touches a circle of radius$$r$$having$$AB$$... IIT-JEE 2009 Paper 2 Offline The tangent$$PT$$and the normal$$PN$$to the parabola$${y^2} = 4ax$$at a point$$P$$on it meet its axis at points$$T$$and$$N$$, respectively.... IIT-JEE 2006 The equations of the common tangents to the parabola$$y = {x^2}$$and$$y = - {\left( {x - 2} \right)^2}$$is/are ## Numerical JEE Advanced 2024 Paper 2 Online A normal with slope \frac{1}{\sqrt{6}} is drawn from the point (0,-\alpha) to the parabola x^2=-4 a y, where a>0. Let L be the line passing ... JEE Advanced 2015 Paper 2 Offline Suppose that the foci of the ellipse$${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$are$$\left( {{f_1},0} \right)$$and$$\left( {{f_2},0} \right)$$w... JEE Advanced 2015 Paper 1 Offline If the normals of the parabola$${y^2} = 4x$$drawn at the end points of its latus rectum are tangents to the circle$${\left( {x - 3} \right)^2} + {\...
JEE Advanced 2015 Paper 1 Offline
Let the curve $$C$$ be the mirror image of the parabola $${y^2} = 4x$$ with respect to the line $$x+y+4=0$$. If $$A$$ and $$B$$ are the points of inte...
IIT-JEE 2012 Paper 1 Offline
Let $$S$$ be the focus of the parabola $${y^2} = 8x$$ and let $$PQ$$ be the common chord of the circle $${x^2} + {y^2} - 2x - 4y = 0$$ and the given p...
IIT-JEE 2011 Paper 1 Offline
Consider the parabola $${y^2} = 8x$$. Let $${\Delta _1}$$ be the area of the triangle formed by the end points of its latus rectum and the point $$P\l... ## MCQ (Single Correct Answer) JEE Advanced 2023 Paper 1 Online Let P be a point on the parabola y^2=4 a x, where a>0. The normal to the parabola at P meets the x-axis at a point Q. The area of the tria... JEE Advanced 2020 Paper 1 Offline Let a, b and$$\lambda $$be positive real numbers. Suppose P is an end point of the latus return of the parabola y2 = 4$$\lambda $$x, and suppose the... JEE Advanced 2019 Paper 2 Offline Let the circles C1 : x2 + y2 = 9 and C2 : (x$$-$$3)2 + (y$$-$$4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x$$-$$... JEE Advanced 2019 Paper 2 Offline Let the circle C1 : x2 + y2 = 9 and C2 : (x$$-$$3)2 + (y$$-$$4)2 = 16, intersect at the points X and Y. Suppose that another circle C3 : (x$$-$$... JEE Advanced 2017 Paper 1 Offline If a tangent to a suitable conic (Column 1) is found to be y = x + 8 and its point of contact is (8, 16), then which of the following options is the o... JEE Advanced 2014 Paper 2 Offline Let$$a, r, s, t$$be nonzero real numbers. Let$$P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)$$and$$S\,\,\left( {a...
JEE Advanced 2014 Paper 2 Offline
Let $$a, r, s, t$$ be nonzero real numbers. Let $$P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)$$ and $$S\,\,\left( {a... JEE Advanced 2013 Paper 2 Offline A line$$L:y=mx+3$$meets$$y$$-axis at R$$(0, 3)$$and the arc of the parabola$${y^2} = 16x,0 \le y \le 6$$at the point$$F\left( {{x_0},{y_0}...
JEE Advanced 2013 Paper 2 Offline
Let $$PQ$$ be a focal chord of the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$P$$ and $$Q$$ meet at a point lying on the line $$y=2x+... JEE Advanced 2013 Paper 2 Offline Let$$PQ$$be a focal chord of the parabola$${y^2} = 4ax$$. The tangents to the parabola at$$P$$and$$Q$$meet at a point lying on the line$$y=2x+...
IIT-JEE 2011 Paper 2 Offline
Let $$(x, y)$$ be any point on the parabola $${y^2} = 4x$$. Let $$P$$ be the point that divides the line segment from $$(0, 0)$$ to $$(x, y)$$ in the ...
IIT-JEE 2009 Paper 2 Offline
The locus of the orthocentre of the triangle formed by the lines $$(1 + p)x - py + p(1 + p) = 0,$$ $$(1 + q)x - qy + q(1 + q) = 0$$ and $$y = 0$$, w...
IIT-JEE 2007
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, re...
IIT-JEE 2007
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, re...
IIT-JEE 2007
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, re...
IIT-JEE 2007
STATEMENT-1: The curve $$y = {{ - {x^2}} \over 2} + x + 1$$ is symmetric with respect to the line $$x=1$$. because STATEMENT-2: A parabola is symmetri...
IIT-JEE 2006
The axis of a parabola is along the line $$y = x$$ and the distances of its vertex and focus from origin are $$\sqrt 2$$ and $$2\sqrt 2$$ respective...
IIT-JEE 2006
Match the following : $$(3, 0)$$ is the pt. from which three normals are drawn to the parabola $${y^2} = 4x$$ which meet the parabola in the points $$... IIT-JEE 2005 Screening Tangent to the curve$$y = {x^2} + 6$$at a point$$(1, 7)$$touches the circle$${x^2} + {y^2} + 16x + 12y + c = 0$$at a point$$Q$$. Then the coord... IIT-JEE 2004 Screening The angle between the tangents drawn from the point$$(1, 4)$$to the parabola$${y^2} = 4x$$is IIT-JEE 2003 Screening The focal chord to$${y^2} = 16x$$is tangent to$${\left( {x - 6} \right)^2} + {y^2} = 2,$$then the possible values of the slope of the chord, are IIT-JEE 2002 Screening The locus of the mid-point of the line segment joining the focus to a moving point on the parabola$${y^2} = 4ax$$is another parabola with directrix IIT-JEE 2002 Screening The equation of the common tangent to the curves$${y^2} = 8x$$and$$xy = - 1$$is IIT-JEE 2001 Screening The equation of the directrix of the parabola$${y^2} + 4y + 4x + 2 = 0$$IIT-JEE 2001 Screening The equation of the common tangent touching the circle$${\left( {x - 3} \right)^2} + {y^2} = 9$$and the parabola$${y^2} = 4x$$above the$$x$$-axis... IIT-JEE 2000 Screening If$$x + y = k$$is normal to$${y^2} = 12x,$$then$$k$$is IIT-JEE 2000 Screening If the line$$x - 1 = 0$$is the directrix of the parabola$${y^2} - kx + 8 = 0,$$then one of the values of$$k$$is IIT-JEE 1999 The curve described parametrically by$$x = {t^2} + t + 1,y = {t^2} - t + 1 $$represents IIT-JEE 1995 Screening Consider a circle with its centre lying on the focus of the parabola$${y^2} = 2px$$such that it touches the directrix of the parabola. Then a point ... ## Subjective IIT-JEE 2004 Tangent is drawn to parabola$${y^2} - 2y - 4x + 5 = 0$$at a point$$P$$which cuts the directrix at the point$$Q$$.$$A$$point$$R$$is such that ... IIT-JEE 2003 Normals are drawn from the point$$P$$with slopes$${m_1}$$,$${m_2}$$,$${m_3}$$to the parabola$${y^2} = 4x$$. If locus of$$P$$with$${m_1}...
IIT-JEE 2000
Let $${C_1}$$ and $${C_2}$$ be respectively, the parabolas $${x^2} = y - 1$$ and $${y^2} = x - 1$$. Let $$P$$ be any point on $${C_1}$$ and $$Q$$ be a...
IIT-JEE 1996
Points $$A, B$$ and $$C$$ lie on the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$A, B$$ and $$C$$, taken in pairs, intersect at points...
IIT-JEE 1996
From a point $$A$$ common tangents are drawn to the circle $${x^2} + {y^2} = {a^2}/2$$ and parabola $${y^2} = 4ax$$. Find the area of the quadrilater...
IIT-JEE 1995
Show that the locus of a point that divides a chord of slope $$2$$ of the parabola $${y^2} = 4x$$ internally in the ratio $$1:2$$ is a parabola. Find ...
IIT-JEE 1994
Through the vertex $$O$$ of parabola $${y^2} = 4x$$, chords $$OP$$ and $$OQ$$ are drawn at right angles to one another . Show that for all positions o...
IIT-JEE 1991
Three normals are drawn from the point $$(c, 0)$$ to the curve $${y^2} = x.$$ Show that $$c$$ must be greater than $$1/2$$. One normal is always the \$...
IIT-JEE 1982
$$A$$ is point on the parabola $${y^2} = 4ax$$. The normal at $$A$$ cuts the parabola again at point $$B$$. If $$AB$$ subtends a right angle at the ve...
IIT-JEE 1981
Suppose that the normals drawn at three different points on the parabola $${y^2} = 4x$$ pass through the point $$(h, k)$$. Show that $$h>2$$.

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IIT-JEE 1994
The point of intersection of the tangents at the ends of the latus rectum of the parabola $${y^2} = 4x$$ is ...... .
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