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Recent questions tagged curves

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GATE IN 2023 | GA Question: 5
In the given diagram, ovals are marked at different heights $(h)$ of a hill. Which one of the following options $\mathbf{P}, \mathbf{Q}, \mathbf{R}$ ... $\mathbf{Q}$\mathbf{R}$\mathbf{S}$
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GATE Mechanical 2020 Set 1 | GA Question: 9
Select the graph that schematically represents BOTH $y=x^{m}\:\text{and}\:y=x^{1/m}$ properly in the interval $0\leq x \leq 1$, for integer values of $m,$ where $m > 1.$
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ISI2014-DCG-27
Let $y^2-4ax+4a=0$ and $x^2+y^2-2(1+a)x+1+2a-3a^2=0$ be two curves. State which one of the following statements is true. ... are tangent to each otherThese two curves intersect orthogonally at one pointThese two curves do not intersect
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ISI2014-DCG-40
Let the following two equations represent two curves $A$ and $B$. $A: 16x^2+9y^2=144\:\: \text{and}\:\: B:x^2+y^2-10x=-21$ Further, let $L$ and $M$ be the ... $ and $M$, is$0^{\circ}$30^{\circ}$45^{\circ}$90^{\circ}$
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ISI2014-DCG-52
The area under the curve $x^2+3x-4$ 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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ISI2015-MMA-47
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 ... xy=k$x^2+y^2=k^2$y^2+2x^2=k^2$x^2-y^2+2yk=k^2$
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ISI2015-MMA-64
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 $t=0$ ... $2 \pi$2 \sqrt{2 \pi}$\sqrt{2 \pi}$none of the above
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ISI2015-MMA-75
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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ISI2015-MMA-86
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 ... $y=\sin 2x$y=\cos 2x+1$y=\sin ^2 x-1$
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ISI2016-DCG-15
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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ISI2016-DCG-16
The set $\{(x,y)\: :\: \mid x\mid+\mid y\mid\:\leq\:1\}$ is represented by the shaded region in
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ISI2016-DCG-40
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$)$ representa circlea parabolaan ellipsea hyperbola
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ISI2016-DCG-44
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$
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ISI2016-DCG-48
The piecewise linear function for the following graph is$f(x)=\begin{cases} = x,x\leq-2 \\ =4,-2<x<3 \\ = x+1,x\geq 3\end{cases}$f(x)=\begin{cases} = x-2,x\leq-2 \\ =4 ...
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ISI2016-DCG-52
The area bounded by $y=x^{2}-4,y=0$ and $x=4$ is$\frac{64}{3}$6$\frac{16}{3}$\frac{32}{3}$
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ISI2018-DCG-26
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$18$
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