Two common tangents to the circle x^{2} + y^{2 }= 2a^{2} and parabola y^{2} = 8ax are [2002]
The normal at the point (bt_{1}^{2} , 2bt^{1}) on a parabola meets the parabola again in the point (bt_{2}^{2}, 2bt_{2}) , then [2003]
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The foci of the ellipse and the hyper bola coincide. Then the value of b^{2} is [2003]
If a ≠ 0 an d the lin e 2bx + 3cy + 4d=0 passes through the points of intersection of the parabolas y^{2 }= 4ax and x^{2 }= 4ay, th en [2004]
The eccentricity of an ellipse, with its centre at the origin, is. If one of the directrices is x = 4 , then the equation ofthe ellipse is: [2004]
Let P be the point ( 1, 0 ) and Q a point on the locus y^{2} = 8x .The locus of mid point of PQ is [2005]
The locus of a point P (α, β) moving under the condition th at the line y = αx + β is a tangen t to the hyper bola is [2005]
An ellipse has OB as semi minor axis, F and F ' its focii and the angle FBF ' is a right angle. Then the eccentricity of the ellipse is [2005]
The locus of the vertices of the family of parabol as [2006]
In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is [2006]
Angle between the tangents to the curve y = x^{2 } 5x+6 at the points (2, 0) and (3, 0) is [2006]
For the Hyper bola which of the following remains constant when a varies = ? [2007]
The equation of a tangent to the parabola y^{2} = 8x is y = x + 2. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is [2007]
The normal to a curve at P(x, y) meets the xaxis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a [2007]
A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is . Then the length of the semimajor axis is [2008]
A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]
The ellipse x^{2} + 4y^{2 }= 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is : [2009]
If two tangents drawn from a point P to the parabola y^{2} = 4x are at right angles, then the locus of P is [2010]
Equation of the ellipse wh ose axes ar e th e axes of coordinates and which passes through the point (–3, 1) and has eccentricity is [2011]
Statement1 : An equation of a common tangent to the parabola y^{2} = 16x and the ellipse 2x^{2} + y^{2 }=4 is y = 2x+ 2
Statement2 : If the line is a common tan gent to the parabola y^{2} = 16x and the ellipse 2x^{2} + y^{2} = 4, then m satisfies m^{4} + 2m^{2} = 24 [2012] [2012]
An ellipse is drawn by taking a diameter of the circle (x – 1)^{2} + y^{2} = 1 as its semiminor axis and a diameter of the circle x^{2} + (y – 2)^{2} = 4 is semimajor axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is : [2012]
The equation of the circle passing through the foci of the ellipse and having centre at (0, 3) is [JEE M 2013]
Given : A circle, 2x^{2} + 2y^{2} = 5 and a parabola,
Statement1 : An equation of a common tangent to these curves is
Statement2 : If the line, is theircommon tangent, then m satisfies m^{4} – 3m^{2} + 2 = 0. [JEE M 2013]
The locus of the foot of perpendicular drawn from the centre of the ellipse x^{2} + 3y^{2 }= 6 on any tangent to it is [JEE M 2014]
The slope of the line touching both the parabolas y^{2} = 4x and x^{2} =32y is [JEE M 2014]
Let O be the vertex and Q be any point on the parabola, x^{2} = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then locus of P is : [JEE M 2015]
The normal to the curve, x^{2} + 2xy – 3y^{2} = 0, at (1, 1) [JEE M 2015]
The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse is : [JEE M 2015]
Let P be the point on the parabola, y^{2} = 8x which is at a minimum distance from the centre C of the circle, x^{2} + (y + 6)^{2} = 1.Then the equation of the circle, passing through C and having its centre at P is: [JEE M 2016]
The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is : [JEE M 2016]
447 docs930 tests

447 docs930 tests
