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Questions >> TN XII Math >> Analytical Geometry

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $x^{2}-3y^{2}+6x+6y+18=0$

answered Jun 25, 2013 by sreemathi.v

1 answer

Prove that the tangent at any point to the rectangular hyperbola forms with the asymptotes a tringle of constant area.

answered Jun 25, 2013 by sreemathi.v

1 answer

Find the equation of the asymptotes of the following rectangular hyperbola $6x^{2}+5xy-6y^{2}+12x+5y+3=0$

answered Jun 25, 2013 by sreemathi.v

1 answer

A cable of a suspension bridge is in the form of a parabola whose span is $40mts$ . The road way is $5mts$ below the lowest point of the cable . if an extra support is provided across the cable $30mts$ above the ground level, Find the length of the support if the height of the pillars are $55mts$ .

answered Jun 25, 2013 by sreemathi.v

1 answer

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $25x^{2}-16y^{2}=400$

answered Jun 25, 2013 by sreemathi.v

1 answer

Find the equation of the asymptotes of the following rectangular hyperbola $2xy+3x+4y+1=0$

answered Jun 25, 2013 by sreemathi.v

1 answer

Find the equation of the asymptotes of the following rectangular hyperbola $xy-kx-hy=0$

answered Jun 25, 2013 by sreemathi.v

1 answer

Find the equation of the rectangular hyperbola which has its center at $(2 , 1 )$ one of its asymptotes $3x-y-5=0$ and which passes through the point $(1 , -1 )$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of parabola if : Vertex $(1 , 4);$ open left ward and passing through the point $(-2,10)$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of parabola if : Vertex $(3 , -2 );$ open downward and the length of the latus rectum is $8$ .

answered Jun 24, 2013 by sreemathi.v

1 answer

A standard rectangular hyperbola has its vertices at $(5 , 7 )$ and $(-3 , -1 )$ find its equation and asymptotes.

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of rectangular hyperbola which has for one of its asymptotes the line $x+2y-5=0$ and passes through the point $(6 , 0 )$ and $(-3 , 0 )$ find its equation and asymptotes

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal at $(-2 , \large\frac{1}{4})$ to the rectangular hyperbola $2xy-2x-8y-1=0$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal at $(3 , 4 )$ to the rectangular hyperbola $xy=12$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of the standard rectangular hyperbola whose centre is $(\large-\frac{1}{2} , -\frac{1}{2})$ and which passes through the point $(1 , \large\frac{1}{4})$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the angle between the asymptotes of hyperbola $4x^{2}-5y^{2}-16x+10y+31=0$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the angle between the asymptotes of hyperbola $9(x-2)^{2}-4(y+3)^{2}=36$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the angle between the asymptotes of hyperbola $24x^{2}-8y^{2}=27$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of the hyperbola if its asymptotes are parallel to $x+2y-12=0$ and $x-2y+8=0, (2 , 4 )$ is the centre of the hyperbola and it passes through $(2 , 0 )$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of the hyperbola if the asymptotes are $2x+3y-8=0$ and $3x-2y+1=0$ and $(5 , 3 )$ is a point on the hyperbola.

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of the asmptotes to the hyperbola $8x^{2}+10xy-3y^{2}-2x+4y-2=0$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation of the asymptotes to the hyperbola $36x^{2}-25y^{2}=900$

answered Jun 24, 2013 by sreemathi.v

1 answer

Find the equation to the chord of contact of tangents from the point $(5 , 3 )$ to the hyperbola $4x^{2}-6y^{2}=24$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation to the chord of contact of tangents from the point $(2 , 4 )$ to the ellipse $2x^{2}+5y^{2}=20$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation to the chord of contact of tangents from the point $(-3 , 1 )$ to the parabola $y^{2}=8x$

answered Jun 21, 2013 by sreemathi.v

1 answer

Show that the line $x-y+4=0$ is a tangent to the ellipse $x^{2}+3y^{2}=12$ . Find the co-ordinates of the point of contact.

answered Jun 21, 2013 by sreemathi.v

1 answer

Prove that the line $5x+12y=9$ touches the hyperbola $x^{2}-9y^{2}=9$ and find its point of contact.

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the two tangents that can be drawn, from the point $(1 , 2 )$ to the hyperbola $2x^{2}-3y^{2}=6$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the two tangents that can be drawn, from the point $(1 , 3 )$ to the ellipse $4x^{2}+9y^{2}=36$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the two tangents that can be drawn,from the point $(2 , -3 )$ to the parabola $y^{2}=4x$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the hyperbola $4x^{2}-y^{2}=64$ ,which are parallel to $10x-3y+9=0$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the ellipse $\large\frac{x^{2}}{20}+\frac{y^{2}}{5}$ $=1,$ Which are perpendicular to $x+y+z=0$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the tangent to the parabola $y^{2}=16x,$ perpendicular to the line $3x-y+8=0$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the tangents to the parabola $y^{2}=6x,$ parallel to $3x-2y+5=0$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the hyperbola $\large\frac{x^{2}}{9}-\frac{y^{2}}{12}=$ $1$ at $\theta=\large\frac{\pi}{6}$

answered Jun 21, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the ellipse $16x^{2}+25y^{2}=400$ at $t=\large\frac{1}{\sqrt{3}}$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the ellipse $x^{2} +4y^{2}=32$ at $\theta=\large\frac{\pi}{4}$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the parabola $y^{2}=8x$ at $t=\large\frac{1}{2}$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the hyperbola $9x^{2}-5y^{2}=31$ at $(2 , -1 )$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the ellipse $2x^{2}+3y^{2}=6$ at $(\sqrt{3} , 0 )$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the parabola $x^{2}+2x-4y+4=0$ at $(0 , 1 )$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the parabola $x^{2}=9y$ at $(3 , 1 )$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the equation of the tangent and normal to the parabola $y^{2}=12x$ at $(3 , -6 )$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $x^{2}-4y^{2}+6x+16y-11=0$

answered Jun 20, 2013 by sreemathi.v

1 answer

Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $\large\frac{y^{2}}{9}-\frac{x^{2}}{25}=$ $1$

answered Jun 20, 2013 by sreemathi.v

1 answer

Show that the locus of a point which moves so that the difference of its distance from the points $(5 , 0 )$ and $(-5 , 0 )$ is $8$ is $9x^{2}-16y^{2}=144$

answered Jun 19, 2013 by sreemathi.v

1 answer

Find the equations of directrices ,latus rectums and length of latus rectum of the following hyperbolas: $9x^{2}-4y^{2}-36x+32y+8=0$

answered Jun 19, 2013 by sreemathi.v

1 answer

Find the equations of directrices ,latus rectums and length of latus rectum of the following hyperbolas: $4x^{2}-9y^{2}=576$

answered Jun 19, 2013 by sreemathi.v

1 answer

Find the equation and the length of the transverse and conjugate axis of the following hyperbola: $16x^{2}-9y^{2}+96x+36y-36=0$

answered Jun 19, 2013 by sreemathi.v

1 answer

Find the equation and the length of the transverse and conjugate axis of the following hyperbola: $8y^{2}-2x^{2}=16$

answered Jun 19, 2013 by sreemathi.v

1 answer

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