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## Parabola

### Mathematics

#### Previous Years Questions

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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...
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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 ...
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From the point ($$-$$1, $$-$$6), two tangents are drawn to y2 = 4x. Then the angle between the two tangents is...
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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 ...
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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...
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A line passes through the point $$( - 1,1)$$ and makes an angle $${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ in the po...
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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 &gt; 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)$$represent... WB JEE 2008 If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the... WB JEE 2008 The length of the common chord of the parabolas y2 = x and x2 = y is WB JEE 2008 If P(at2, 2at) be one end of a focal chord of the parabola y2 = 4ax, then the length of the chord is... WB JEE 2008 The vertex of the parabola x2 + 2y = 8x$$-$$7 is WB JEE 2008 The two parabolas x2 = 4y and y2 = 4x meet in two distinct points. One of these is the origin and the other is... WB JEE 2008 ## Subjective More Find the angle subtended by the double ordinate of length 2a of the parabola y2 = ax at its vertex. WB JEE 2009 Prove that for all values of m, except zero the st. line$$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...
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