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WB JEE

Parabola

Mathematics

Previous Years Questions

MCQ (Single Correct Answer)

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If P1P2 and P3P4 are two focal chords of the parabola y2 = 4ax then the chords P1P3 and P2P4 intersect on the...
WB JEE 2022
Let the tangent and normal at any point P(at2, 2at), (a > 0), on the parabola y2 = 4ax meet the axis of the parabola at ...
WB JEE 2022
From the point ($$-$$1, $$-$$6), two tangents are drawn to y2 = 4x. Then the angle between the two tangents is...
WB JEE 2022
AB is a chord of a parabola y2 = 4ax, (a > 0) with vertex A. BC is drawn perpendicular to AB meeting the axis at C. The ...
WB JEE 2022
Let P be a point on (2, 0) and Q be a variable point on (y $$-$$ 6)2 = 2(x $$-$$ 4). Then the locus of mid-point of PQ i...
WB JEE 2022
A line passes through the point $$( - 1,1)$$ and makes an angle $${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ in the po...
WB JEE 2022
The point of contact of the tangent to the parabola y2 = 9x which passes through the point (4, 10) and makes an angle $$...
WB JEE 2022
From a point (d, 0) three normal are drawn to the parabola y2 = x, then
WB JEE 2021
The locus of the vertices of the family of parabolas $$6y = 2{a^3}{x^2} + 3{a^2}x - 12a$$ is
WB JEE 2021
If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through ($$ - $...
WB JEE 2020
The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12. ...
WB JEE 2020
The length of the chord of the parabola y2 = 4ax(a > 0) which passes through the vertex and makes an acute angle $$\a...
WB JEE 2020
The locus of the middle points of all chords of the parabola y2 = 4ax passing through the vertex is
WB JEE 2011
The coordinates of a moving point P are (2t2 + 4, 4t + 6). Then its locus will be a/an
WB JEE 2011
The vertex of the parabola y2 + 6x $$-$$ 2y + 13 = 0 is
WB JEE 2011
If t1 and t2 be the parameters of the end points of a focal chord for the parabola y2 = 4ax, then which one is true?...
WB JEE 2010
The coordinates of the focus of the parabola described parametrically by x = 5t2 + 2, y = 10t + 4 are
WB JEE 2009
The latus rectum of an ellipse is equal to one-half of its minor axis. The eccentricity of the ellipse is
WB JEE 2008
The equation of the ellipse having vertices at ($$\pm$$ 5, 0) and foci ($$\pm$$ 4, 0) is
WB JEE 2008
If t is a parameter, then $$x = a\left( {t + {1 \over t}} \right)$$, $$y = b\left( {t - {1 \over t}} \right)$$ represent...
WB JEE 2008
If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the...
WB JEE 2008
The length of the common chord of the parabolas y2 = x and x2 = y is
WB JEE 2008
If P(at2, 2at) be one end of a focal chord of the parabola y2 = 4ax, then the length of the chord is...
WB JEE 2008
The vertex of the parabola x2 + 2y = 8x $$-$$ 7 is
WB JEE 2008
The two parabolas x2 = 4y and y2 = 4x meet in two distinct points. One of these is the origin and the other is...
WB JEE 2008

Subjective

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Find the angle subtended by the double ordinate of length 2a of the parabola y2 = ax at its vertex.
WB JEE 2009
Prove that for all values of m, except zero the st. line $$y = mx + {a \over m}$$ touches the parabola y2 = 4ax...
WB JEE 2008
If the tangent to the parabola y = x(2 $$-$$ x) at the point (1, 1) intersects the parabola at P. Find the co-ordinate o...
WB JEE 2008

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