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Recent questions tagged curves
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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
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Sep 23, 2019
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Geometry
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Arjun
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isi2014dcg
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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 $0^{\circ}$ $30^{\circ}$ $45^{\circ}$ $90^{\circ}$
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Sep 23, 2019
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Others
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Arjun
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isi2014dcg
curves
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3
ISI2014DCG52
The area under the curve $x^2+3x4$ in the positive quadrant and bounded by the line $x=5$ is equal to $59 \frac{1}{6}$ $61 \frac{1}{3}$ $40 \frac{2}{3}$ $72$
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Sep 23, 2019
in
Geometry
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Arjun
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isi2014dcg
curves
area
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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 $xy=k$ $x^2+y^2=k^2$ $y^2+2x^2=k^2$ $x^2y^2+2yk=k^2$
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Sep 23, 2019
in
Geometry
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Arjun
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isi2015mma
curves
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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
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Sep 23, 2019
in
Geometry
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Arjun
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isi2015mma
trigonometry
curves
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6
ISI2015MMA75
The length of the curve $x=t^3$, $y=3t^2$ from $t=0$ to $t=4$ is $5 \sqrt{5}+1$ $8(5 \sqrt{5}+1)$ $5 \sqrt{5}1$ $8(5 \sqrt{5}1)$
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Sep 23, 2019
in
Geometry
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Arjun
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isi2015mma
curves
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0
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1
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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 $y=1/2 \cos ^2 x$ $y=\sin 2x$ $y=\cos 2x+1$ $y=\sin ^2 x1$
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Sep 23, 2019
in
Geometry
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Arjun
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isi2015mma
trigonometry
curves
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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 $ $y\:\leq\: \mid x\:\mid$ $\mid \:y\mid\: \leq\: x$
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Sep 18, 2019
in
Geometry
by
gatecse
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17.5k
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13
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isi2016dcg
area
curves
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0
votes
1
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9
ISI2016DCG16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
asked
Sep 18, 2019
in
Geometry
by
gatecse
Boss
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17.5k
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11
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isi2016dcg
curves
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0
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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, 2019
in
Geometry
by
gatecse
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17.5k
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14
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isi2016dcg
trigonometry
curves
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11
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, 2019
in
Geometry
by
gatecse
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17.5k
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isi2016dcg
hyperbola
curves
nongate
0
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0
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12
ISI2016DCG48
The piecewise linear function for the following graph is $f(x)=\begin{cases} = x,x\leq2 \\ =4,2<x<3 \\ = x+1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = x2,x\leq2 \\ =4,2<x<3 \\ = x1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = 2x,x\leq2 \\ =x,2<x<3 \\ = x+1,x\geq 3\end{cases}$ $f(x)=\begin{cases} = 2x,x\leq2 \\ =4,2<x<3 \\ = x+1,x\geq 3\end{cases}$
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Sep 18, 2019
in
Calculus
by
gatecse
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14
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isi2016dcg
calculus
functions
curves
nongate
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13
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, 2019
in
Geometry
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gatecse
Boss
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17.5k
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isi2016dcg
curves
area
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0
votes
1
answer
14
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, 2019
in
Geometry
by
gatecse
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56
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isi2018dcg
curves
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