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Recent questions tagged curves
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1
ISI2014DCG27
Let $y^24ax+4a=0$ and $x^2+y^22(1+a)x+1+2a3a^2=0$ be two curves. State which one of the following statements is true. These two curves intersect at two points These two curves are tangent to each other These two curves intersect orthogonally at one point These two curves do not intersect
asked
Sep 23
in
Others
by
Arjun
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isi2014dcg
curves
0
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1
answer
2
ISI2014DCG40
Let the following two equations represent two curves $A$ and $B$. $A: 16x^2+9y^2=144\:\: \text{and}\:\: B:x^2+y^210x=21$ Further, let $L$ and $M$ be the tangents to these curves $A$ and $B$, respectively, at the point $(3,0)$. Then the angle between these two tangents, $L$ and $M$, is $0^{\circ}$ $30^{\circ}$ $45^{\circ}$ $90^{\circ}$
asked
Sep 23
in
Others
by
Arjun
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425k
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10
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isi2014dcg
curves
tangents
angles
0
votes
0
answers
3
ISI2015MMA46
If the tangent at the point $P$ with coordinates $(h,k)$ on the curve $y^2=2x^3$ is perpendicular to the straight line $4x=3y$, then $(h,k) = (0,0)$ $(h,k) = (1/8, 1/16)$ $(h,k) = (0,0) \text{ or } (h,k) = (1/8, 1/16)$ no such point $(h,k)$ exists
asked
Sep 23
in
Geometry
by
Arjun
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425k
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7
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isi2015mma
straight
line
tangent
curves
0
votes
0
answers
4
ISI2015MMA47
Consider the family $\mathcal{F}$ of curves in the plane given by $x=cy^2$, where $c$ is a real parameter. Let $\mathcal{G}$ be the family of curves having the following property: every member of $\mathcal{G}$ intersect each member of $\mathcal{F}$ orthogonally. Then $\mathcal{G}$ is given by $xy=k$ $x^2+y^2=k^2$ $y^2+2x^2=k^2$ $x^2y^2+2yk=k^2$
asked
Sep 23
in
Geometry
by
Arjun
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425k
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5
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isi2015mma
curves
0
votes
0
answers
5
ISI2015MMA64
Let the position of a particle in three dimensional space at time $t$ be $(t, \cos t, \sin t)$. Then the length of the path traversed by the particle between the times $t=0$ and $t=2 \pi$ is $2 \pi$ $2 \sqrt{2 \pi}$ $\sqrt{2 \pi}$ none of the above
asked
Sep 23
in
Geometry
by
Arjun
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425k
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isi2015mma
trigonometry
curves
nongate
0
votes
0
answers
6
ISI2015MMA75
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is $5 \sqrt{5}+1$ $8(5 \sqrt{5}+1)$ $5 \sqrt{5}1$ $8(5 \sqrt{5}1)$
asked
Sep 23
in
Geometry
by
Arjun
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425k
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6
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isi2015mma
curves
nongate
0
votes
1
answer
7
ISI2015MMA86
The coordinates of a moving point $P$ satisfy the equations $\frac{dx}{dt} = \tan x, \:\:\:\: \frac{dy}{dt}=\sin^2x, \:\:\:\:\: t \geq 0.$ If the curve passes through the point $(\pi/2, 0)$ when $t=0$, then the equation of the curve in rectangular coordinates is $y=1/2 \cos ^2 x$ $y=\sin 2x$ $y=\cos 2x+1$ $y=\sin ^2 x1$
asked
Sep 23
in
Geometry
by
Arjun
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425k
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12
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isi2015mma
trigonometry
curves
nongate
0
votes
0
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8
ISI2016DCG15
The shaded region in the following diagram represents the relation $y\:\leq\: x$ $\mid \:y\mid \:\leq\: \mid x\:\mid $ $y\:\leq\: \mid x\:\mid$ $\mid \:y\mid\: \leq\: x$
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

7
views
isi2016dcg
area
curves
nongate
0
votes
1
answer
9
ISI2016DCG16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

6
views
isi2016dcg
curves
area
nongate
0
votes
0
answers
10
ISI2016DCG40
The equations $x=a\cos\theta+b\sin\theta$ and $y=a\sin\theta+b\cos\theta,(0\leq\theta\leq2\pi$ and $a,b$ are arbitrary constants$)$ represent a circle a parabola an ellipse a hyperbola
asked
Sep 18
in
Geometry
by
gatecse
Boss
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16.8k
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7
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isi2016dcg
trigonometry
curves
nongate
0
votes
0
answers
11
ISI2016DCG42
In an ellipse, the distance between its foci is $6$ and its minor axis is $8.$ Then its eccentricity is $\frac{4}{5}$ $\frac{1}{\sqrt{52}}$ $\frac{3}{5}$ $\frac{1}{2}$
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
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3
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isi2016dcg
ellipse
eccentricity
curves
nongate
0
votes
0
answers
12
ISI2016DCG44
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2},$ then the equation of the hyperbola is $y^{2}x^{2}=32$ $x^{2}y^{2}=16$ $y^{2}x^{2}=16$ $x^{2}y^{2}=32$
asked
Sep 18
in
Geometry
by
gatecse
Boss
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16.8k
points)

3
views
isi2016dcg
hyperbola
curves
nongate
0
votes
0
answers
13
ISI2016DCG48
The piecewise linear function for the following graph is $f(x)=\begin{cases} = x,x\leq2 \\ =4,2<x<3 \\ = x+1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = x2,x\leq2 \\ =4,2<x<3 \\ = x1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = 2x,x\leq2 \\ =x,2<x<3 \\ = x+1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = 2x,x\leq2 \\ =4,2<x<3 \\ = x+1,x\geq 3\end{cases}$
asked
Sep 18
in
Calculus
by
gatecse
Boss
(
16.8k
points)

7
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isi2016dcg
calculus
functions
curves
nongate
0
votes
0
answers
14
ISI2016DCG52
The area bounded by $y=x^{2}4,y=0$ and $x=4$ is $\frac{64}{3}$ $6$ $\frac{16}{3}$ $\frac{32}{3}$
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

4
views
isi2016dcg
curves
area
nongate
0
votes
1
answer
15
ISI2018DCG26
The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$axis in the first quadrant is $9$ $\frac{27}{4}$ $36$ $18$
asked
Sep 18
in
Geometry
by
gatecse
Boss
(
16.8k
points)

38
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isi2018dcg
curves
area
nongate
+1
vote
0
answers
16
ISI2016MMA26
Let $x$ and $y$ be real numbers satisfying $9x^2+16y^2=1$. Then $(x+y)$ is maximum when $y=9x/16$ $y=9x/16$ $y=4x/3$ $y=4x/3$
asked
Sep 13, 2018
in
Others
by
jothee
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105k
points)

7
views
isi2016mmamma
curves
nongate
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Really helpful sir Thanks a tonππ
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