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Recent questions and answers in Analytical Geometry
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TN XII Math
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Analytical Geometry
Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $x^{2}-3y^{2}+6x+6y+18=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q5
q5-4
modelpaper
mar-2008
oct-2008
oct-2009
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.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q7
modelpaper
mar-2006
oct-2007
answered
Jun 25, 2013
by
sreemathi.v
1
answer
Find the equation of the asymptotes of the following rectangular hyperbola $6x^{2}+5xy-6y^{2}+12x+5y+3=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q6
q6-3
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 $55mts$.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-1
p193
q5
jun-2006
oct-2007
modelpaper
answered
Jun 25, 2013
by
sreemathi.v
1
answer
Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $25x^{2}-16y^{2}=400$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q5
q5-1
answered
Jun 25, 2013
by
sreemathi.v
1
answer
Find the equation of the asymptotes of the following rectangular hyperbola $2xy+3x+4y+1=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q6
q6-2
answered
Jun 25, 2013
by
sreemathi.v
1
answer
Find the equation of the asymptotes of the following rectangular hyperbola $xy-kx-hy=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q6
q6-1
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 $(1 , -1 )$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q5
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 $(-2,10)$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-1
q1
q1-6
p192
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 $8$.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-1
p192
q1
q1-7
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.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q4
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
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q3
modelpaper
mar-2007
mar-2008
oct-2008
oct-2006
jun-2007
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 $
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q2
q2-2
answered
Jun 24, 2013
by
sreemathi.v
1
answer
Find the equation of the tangent and normal at $(3 , 4 )$ to the rectangular hyperbola $xy=12$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q2
q2-1
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 $(1 , \large\frac{1}{4})$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-6
p262
q1
answered
Jun 24, 2013
by
sreemathi.v
1
answer
Find the angle between the asymptotes of hyperbola $4x^{2}-5y^{2}-16x+10y+31=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-5
p257
q3
q3-3
answered
Jun 24, 2013
by
sreemathi.v
1
answer
Find the angle between the asymptotes of hyperbola $9(x-2)^{2}-4(y+3)^{2}=36$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-5
p257
q3
q3-2
answered
Jun 24, 2013
by
sreemathi.v
1
answer
Find the angle between the asymptotes of hyperbola $24x^{2}-8y^{2}=27$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-5
p257
q3
q3-1
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 $(2 , 0 )$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-5
p257
q2
q2-2
mar-2006
mar-2009
jun-2008
jun-2006
modelpaper
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.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-5
p257
q2
q2-1
modelpaper
mar-2008
oct-2008
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$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-5
p257
q1
q1-2
answered
Jun 24, 2013
by
sreemathi.v
1
answer
Find the equation of the asymptotes to the hyperbola $36x^{2}-25y^{2}=900$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-5
p257
q1
q1-1
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 $4x^{2}-6y^{2}=24$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q7
q7-3
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 $2x^{2}+5y^{2}=20$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q7
q7-2
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 $y^{2}=8x$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q7
q7-1
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.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q6
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.
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q5
jun-2009
modelpaper
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 $2x^{2}-3y^{2}=6$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q4
q4-3
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 $4x^{2}+9y^{2}=36$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q4
q4-2
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 $
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q4
q4-1
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 $10x-3y+9=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q3
q3-4
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}$$=1,$ Which are perpendicular to $ x+y+z=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q3
q3-3
answered
Jun 21, 2013
by
sreemathi.v
1
answer
Find the equation of the tangent to the parabola $y^{2}=16x,$ perpendicular to the line $3x-y+8=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q3
q3-2
answered
Jun 21, 2013
by
sreemathi.v
1
answer
Find the equation of the tangents to the parabola $y^{2}=6x,$ parallel to $3x-2y+5=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p249
q3
q3-1
answered
Jun 21, 2013
by
sreemathi.v
1
answer
Find the equation of the tangent and normal to the hyperbola $\large\frac{x^{2}}{9}-\frac{y^{2}}{12}=$$1$ at $\theta=\large\frac{\pi}{6}$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q2
q2-4
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 $t=\large\frac{1}{\sqrt{3}}$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q2
q2-3
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 $\theta=\large\frac{\pi}{4}$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q2
q2-2
answered
Jun 20, 2013
by
sreemathi.v
1
answer
Find the equation of the tangent and normal to the parabola $y^{2}=8x $ at $t=\large\frac{1}{2}$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q2
q2-1
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 $(2 , -1 )$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q1
q1-5
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 )$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q1
q1-4
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 $(0 , 1 )$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q1
q1-3
answered
Jun 20, 2013
by
sreemathi.v
1
answer
Find the equation of the tangent and normal to the parabola $x^{2}=9y$ at $(3 , 1 )$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q1
q1-2
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 )$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-4
p248
q1
q1-1
answered
Jun 20, 2013
by
sreemathi.v
1
answer
Find the eccentricity, centre , foci , and vertices of the following hyperbolas and draw their diagrams: $x^{2}-4y^{2}+6x+16y-11=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q5
q5-3
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$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q5
q5-2
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 $9x^{2}-16y^{2}=144$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q4
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:$9x^{2}-4y^{2}-36x+32y+8=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q3
q3-2
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: $4x^{2}-9y^{2}=576$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q3
q3-1
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:$16x^{2}-9y^{2}+96x+36y-36=0$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q2
q2-3
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: $8y^{2}-2x^{2}=16$
tnstate
class12
bookproblem
ch4
sec-1
exercise4-3
p238
q2
q2-2
answered
Jun 19, 2013
by
sreemathi.v
1
answer
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