Recent questions tagged coordinate-geometry-conic -sections

If vertex and focus of hyperbola are $(2,3)$ and $(6,3)$ respectively and eccentricity e of the hyperbola is 2 then equation of the hyperbola is

asked Apr 21, 2014 by meena.p

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Equation of the hyperbola with eccentricity $\large\frac{3}{2}$ and foci at $(\pm2,0)$ is

asked Apr 21, 2014 by meena.p

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The eccentricity of the hyperbola $9y^2 -4x^2=36$ is

asked Apr 21, 2014 by meena.p

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The distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt 2$. Its equation is

asked Apr 21, 2014 by meena.p

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Equation of the chord of the hyperbola $25x^2-16y^2=400$ which is bisected at the point $(6,2)$ is

asked Apr 21, 2014 by meena.p

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Find the equation of hyperbola if the distance between the foic is $16, e=\sqrt 2$ and axis along x-axis with centre oxgin.

asked Apr 21, 2014 by meena.p

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Find the equation of the tangents drawn from the point $(-1,-2)$ to the hyperbola $2x^2-3y^2=6 $

asked Apr 21, 2014 by meena.p

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A rectangular hyperbola whose cetre is C is cut by any circle of radius r in four points $P,Q,R$ and S. Then $CP^2+CQ^2+CR2+CS^2$ is equal to.

asked Apr 21, 2014 by meena.p

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If angle between the asymptotcs of the hyperbola $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$is $45^{\circ}$ then value of eccentricity $e$ is :

asked Apr 21, 2014 by meena.p

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Equation of chord of the hyperbola $25x^2-16y^2=400$ which is bisected at the point $(6,2)$ is

asked Apr 21, 2014 by meena.p

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If $e$ and $e'$ be the eccentricities of a hyperbola and its conjugate then $ \large\frac {1}{e^2}+\frac{1}{e^{12}}$ is equal to

asked Apr 21, 2014 by meena.p

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The locus of a point $p(\alpha, \beta)$ moving under the condition that the line $y=\alpha x + \beta$ is a tangent to the hyperbola $\large\frac{x^2}{a^2} -\frac{y^2}{b^2}$$=1$ is

asked Apr 21, 2014 by meena.p

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A circle touches the x-axis and also touches the circle with centre at $(0,3)$ and radius the circle with centre at $(0,3)$ and radius 2. The locus of the center of circle is

asked Apr 21, 2014 by meena.p

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If the foci of the ellipse $\large\frac{x^2}{16}+\frac{y^6}{b^2}$$=1$ and the hyperbola. $\large\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}$ coincide, then the value of $b^2$ is

asked Apr 21, 2014 by meena.p

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Angle between the asymptotes of the hyperbola $3x^2+7xy+2y^2-11x-7y+10=0$ is

asked Apr 21, 2014 by meena.p

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If $e_1$ and $e_2$ are the eccentricities of the hyperbolas $\large\frac{x^2}{a^2}-\frac{y^2}{b^2}$$=1$ and $\large\frac{y^2}{b^2}-\frac{x^2}{a^2}$$=1$ Then value of $\large\frac{1}{e_1^2}+\frac{1}{e_2^2}$ is

asked Apr 21, 2014 by meena.p

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The vertices of the hyperbola $9x^2-16y^2-36x+96y-252=0$ are

asked Apr 11, 2014 by meena.p

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The diameter of $16x^2-9y^2=144$ which is conjugate to $x=2y$ is

asked Apr 11, 2014 by meena.p

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A common tangent to $9x^2-16y^2=144$ and $x^2+y^2=9$ is

asked Apr 11, 2014 by meena.p

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The eccentricity of the hyperbola whose latus rectum is $8$ and conjugate axis is equal to half the distance between the foci is

asked Apr 11, 2014 by meena.p

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Find the asymptotes of the hyperbola. $xy=4x+3y$

asked Apr 11, 2014 by meena.p

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Find the equation of the hyperbola with focus $(2,2) \; e=2$ and directrise $x+y=9$

asked Apr 10, 2014 by meena.p

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The minimum area of triangle formed by the tangents to the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ coordinate axes is :

asked Apr 10, 2014 by meena.p

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The locus of the mid- points of the portion of the tangents to the ellipse intercepted between the axis is :

asked Apr 10, 2014 by meena.p

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The equation of the ellipse (referred to its axis as the axis of x and y respectively) which passes through the point $(-3,1)$ and had eccentricity $\sqrt {\large\frac{ 2}{5}}$

asked Apr 10, 2014 by meena.p

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The eccentric angle of a point on the ellipse $\large\frac{x^2}{6} +\frac{y^2}{2}$$=1$ Whose distance from the centre of ellipse is 2 is

asked Apr 10, 2014 by meena.p

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Find the equation of tangent to the ellipse $3x^2+4y^2=12$ which are parallel to the line $y+2x=4$

asked Apr 10, 2014 by meena.p

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P is a point, two tangents are drawn from it to the parabola $y^2=4x$ such that the slope of one tangent is three times the slope of the other. The locus of P is

asked Apr 10, 2014 by meena.p

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If the vertex and the focus of a parabola are $(-1,1)$ and $(2,3)$ respectively then the equation of the directrise , is

asked Apr 10, 2014 by meena.p

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The angle between the tangent drawn from the point $(1,4)$ to the parabola $y^2=4x$ is

asked Apr 10, 2014 by meena.p

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The curve disturbed parametrically by $x=t^2+t+1\;y=t^2-t+1$ represents

asked Apr 10, 2014 by meena.p

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If $x+y=k$ is the normal to $y^2=12x$ then k is

asked Apr 10, 2014 by meena.p

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If the line $x-1=0$ is the directrix of parabola $y^2-kx+8=0$ then one of the value of k is

asked Apr 10, 2014 by meena.p

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The equation of the directrise of the parabola $y^2+4y+4x+2=0$ is

asked Apr 10, 2014 by meena.p

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The angle between the tangents draw from the origin to the parabola $y^2=4a(x-a)$ is

asked Apr 10, 2014 by meena.p

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The equation of common tangent to the curves $y^2=8x$ and $xy=-1$ is

asked Apr 10, 2014 by meena.p

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The locus of the mid point of the line segment joining the focus to a moving point on parabola $y^2=4ax$ is another parabola with direction

asked Apr 9, 2014 by meena.p

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In the parabola $y^2=4ax$ , the length of the chord passing through the vertex and inclined to the x-axis at an angle $\theta$ is

asked Apr 9, 2014 by meena.p

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The normal to the parabola $y^2=8x$ at the point $(2,4)$ meets the parabola again at the point.

asked Apr 9, 2014 by meena.p

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The focus of the parabola $y^2-x-2y+2=0$ is

asked Apr 9, 2014 by meena.p

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If polar of the parabola $x^2=4ay$ is always touching the parabola $y^2=4ax$ then locus of the pole is :

asked Apr 9, 2014 by meena.p

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Equation of the parabola if its vertex and focus are $(-2,3)$ and $(1,-1)$ respectively is

asked Apr 9, 2014 by meena.p

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Line $y=mx+c$ will touch the parabola <Br> $\qquad \qquad \qquad x^2=4ay$ if,

asked Apr 9, 2014 by meena.p

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The common tangent to the parabola $y^2=4ax$ and $x^2=4ay$ is

asked Apr 9, 2014 by meena.p

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The normal at $(a,2a)$ on $y^2=4ax$ meets the curve again at $(at^2,2at)$ then the value of t is

asked Apr 9, 2014 by meena.p

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If the parabolas $Y^2= 4x$ and $x^2=32y$ intersect at $(16,8)$ at an angle $\theta$ then $\theta$ is equal to

asked Apr 9, 2014 by meena.p

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The length of a focal chord of the parabola $y^2=4ax$ making an angle $\theta$ with the axis of the parabola is

asked Apr 9, 2014 by meena.p

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The ratio in which the line segment joining the points $(4,-6)$ and $(3,1)$ is divided by the parabola $y^2=4ax$ is

asked Apr 9, 2014 by meena.p

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Find the points of the conic $y=x^2+7x+2$ which is nearest to the line $3x-y-3=0$

asked Apr 9, 2014 by meena.p

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Find the equation of the chord of the parabola $y^2=12x$ which is bisected at $(5,-7)$

asked Apr 9, 2014 by meena.p

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