Recent questions tagged tnstate

The difference between the focal dintences of any point on the hyperbola $\large\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=$$1$ is $24$ and the eccentricity is $2$. Then the equation of the hyperbola is

asked May 14, 2013 by poojasapani_1

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The eccentricity of the hyperbola $ 12y^{2}-4x^{2}-24x+48y-127=0$ is

asked May 14, 2013 by poojasapani_1

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The eccentricity of the hyperbola whose latus rectum is equal to half of its conjugate axis is

asked May 14, 2013 by poojasapani_1

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The locus of foot of perpendicular from the focus to a tangent of the curve $ 16x^{2}+25y^{2}=400$ is

asked May 13, 2013 by poojasapani_1

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The radius of the director circle of the conic $9x^{2}+16y^{2}=144 $ is

asked May 13, 2013 by poojasapani_1

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The sum of the distance of any point on the ellipse $ 4x^{2}+9y^{2}=36 $ from $(\sqrt{5},0) and (-\sqrt{5} ,0) $ is

asked May 13, 2013 by poojasapani_1

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The straight line $2x-y+c=0$ is a tangent to the ellipse $ 4x^{2}+8y^{2}=32$ if $c$ is

asked May 13, 2013 by poojasapani_1

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If the length of major and semi-minor axis of an ellipse are $8 , 2 $ and their corresponding equations are $y-6=0 $ and $x+4=0 $ then the equations of the ellipse is

asked May 13, 2013 by poojasapani_1

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The distance between the foci of the ellipse $9x^{2}+5y^{2}=180 $ is

asked May 13, 2013 by poojasapani_1

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The length of the semi-major and the length of the semi-minor axis of the ellipse $\large\frac{x^{2}}{144}+\frac{y^{2}}{169}$=$1$ are

asked May 13, 2013 by poojasapani_1

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The eccentricity of the conic $9x^{2}+5y^{2}-54x-40y+116=0 $ is

asked May 13, 2013 by poojasapani_1

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The angle between the two tangents drawn from the point $(-4 , 4)$ to $y^{2}=16x $ is

asked May 13, 2013 by poojasapani_1

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The tangents at the end of any focal chord to the parabola $y^{2}=12x$ intersect on the line

asked May 13, 2013 by poojasapani_1

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The line $ 2x+3y+9=0$ touches the parabola $y^{2}=8x$ at the point

asked May 13, 2013 by poojasapani_1

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The vertex of the parabola $ x^{2}=8y-1$ is

asked May 13, 2013 by poojasapani_1

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The focus of the parabola $x^{2}=16y$ is

asked May 13, 2013 by poojasapani_1

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The length of the latus rectum of the parabola whose vertex is $(2 ,-3)$ and the directrix $ x=4 $ is

asked May 13, 2013 by poojasapani_1

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The diretrix of the parabola $y^{2}=x+4$ is

asked May 13, 2013 by poojasapani_1

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The length of the latus rectum of the parabola $y^{2}-4x+4y+8=0$ is

asked May 13, 2013 by poojasapani_1

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The point of intersection of the tangents at $t_{1}=t $ and $t_{2}=3t$ to the parabola $y^{2}=8x $ is

asked May 13, 2013 by poojasapani_1

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The line $4x+2y=c$ is a tangent to the parabola $y^{2}=16x$ then $c$ is

asked May 13, 2013 by poojasapani_1

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$16x^{2}-3y^{2}-32x-12y-44=0 $ represents

asked May 13, 2013 by poojasapani_1

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The axis of the parabola $y^{2}-2y+8x-23=0$ is

asked May 13, 2013 by poojasapani_1

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If $\omega$ is a cube root of unity then the value of $(1-\omega)(1-\omega^{2})(1-\omega^{4})(1-\omega^{8})$ is

asked May 13, 2013 by poojasapani_1

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If $\omega$ is the $n$th root of unity then

asked May 13, 2013 by poojasapani_1

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If $\omega$ is a cube root of unity then the value of $(1-\omega+\omega^{2})^{4}+(1+\omega-\omega^{2})^{4}$ is

asked May 13, 2013 by poojasapani_1

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If$ -i+3 $ is a root of $x^{2}-6x+k=0 $ then the value of $k$ is

asked May 13, 2013 by poojasapani_1

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If $\large\frac{1-i}{1+i}$ is a root of the equation $ax^{2}+bx+1=0$ where $a ,b $ are real then $(a , b) $is

asked May 13, 2013 by poojasapani_1

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The equation having $4-3j$ and $4+3j $ as roots is

asked May 13, 2013 by poojasapani_1

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The quadratic equation whose roots are $\pm\;i\sqrt{7} $is

asked May 13, 2013 by poojasapani_1

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If $-i+2 $ is one root of the equation $ax^{2}-bx+c=0$, then the other root is

asked May 13, 2013 by poojasapani_1

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The conjugate of $i^{13}+i^{14}+i^{15}+i^{16}$ is

asked May 12, 2013 by poojasapani_1

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The value of $i+i^{22}+i^{23}+i^{24}+i^{25}$ is

asked May 12, 2013 by poojasapani_1

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$z_{1}=4+5i,z_{2}=-3+2i$ then $\large\frac{z_{1}}{z_{2}}$is

asked May 12, 2013 by poojasapani_1

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If $ a=\cos\alpha- i \sin \alpha,b=\cos\beta-i \sin\beta,c=\cos\gamma-i\sin\gamma$ then $(a^{2} c^{2} -b^{2})/abc$ is

asked May 12, 2013 by poojasapani_1

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If $x=\cos\theta+i\sin\theta $ the value of $x^{n}+\large\frac{1}{x^{n}}$ is

asked May 12, 2013 by poojasapani_1

1 answer

If $-\overline{z}$ lies in the third quadrant then $z$ lies in the

asked May 12, 2013 by poojasapani_1

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If $z_{n}=\cos\large\frac{n\pi}{3}$$+i\sin\large\frac{n\pi}{3} $ then $z_{1}z_{2} \dots\;z_{6}$is

asked May 12, 2013 by poojasapani_1

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$\large\frac{1+e^{-i\theta}}{1+e^{i\theta}}$=

asked May 12, 2013 by poojasapani_1

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If $p$ represents the veriable complex number $z$ and if $|2z-1|=2|z|$ then the locus of $p$ is

asked May 12, 2013 by poojasapani_1

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The polar form of the complex number $(i^{25})^{3}$ is

asked May 12, 2013 by poojasapani_1

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If the point represented by the complex number $iz$ is rotated about the origin through the angle $\large\frac{\pi}{2}$ in the counter clockwise direction then the complex number representing the new position is

asked May 12, 2013 by poojasapani_1

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If the amplitude of a complex number is $\pi/2$ then the number is

asked May 12, 2013 by poojasapani_1

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If $z$ represents a complex number then arg $(z)+arg(\overline{z})$ is

asked May 12, 2013 by poojasapani_1

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The points $z_{1} , z_{2} , z_{3} , z_{4} $ in the complex plane are the vertices of a parallelogram taken in order if and only if

asked May 12, 2013 by poojasapani_1

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If $a=3+i $ and $z=2-3i$ then the points on the Argand diagram representing $az , 3az $ and $-az $ are

asked May 12, 2013 by poojasapani_1

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If $A+iB=(a_{1}+ib_{1})(a_{2}+ib_{2})(a_{3}+ib_{3}) $ then $A^{2}+B^{2}$is

asked May 11, 2013 by poojasapani_1

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The modulus of the complex number $2+i\sqrt{3}$ is

asked May 11, 2013 by poojasapani_1

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If $x^{2}+y^{2}=1$ then the value of $\large\frac{1+x+iy}{1+x-iy}$ is

asked May 11, 2013 by poojasapani_1

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If $(m-5)+i(n+4)$ is the complex conjugate of $(2m+3)+i(3n-2)$ then $(n ,m )$are

asked May 11, 2013 by poojasapani_1

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