Recent questions tagged p192

Find the equation of parabola if : Vertex $(1 , 4); $ open left ward and passing through the point $(-2,10)$

asked Jun 24, 2013 by sreemathi.v

1 answer

If a parabolic reflector is $20cm$ in diameter and $5cm$ deep, find the distance of the focus from the centre of the reflector.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $x^{2}-6x-12y-3=0$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $y^{2}+8x-6y+1=0$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $(x-4)^{2}=4(y+2).$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs.$x^{2}=20y $

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $y^{2}=-8x$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(2 , 3 )$ open upward ;and passing through the point $(6 , 4 )$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if :Vertex $(3 , -1 );$ open rightward ; the distance between the latus recturm and directrix is $4$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(3 , -2 ); $ open downward and the length of the latus rectum is $8$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(1 , 2 ) ;$ latus recturm :$y=5$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(1 , 4 );$ focus :$(-2 , 4 ).$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(0 , 0 ); $ focus : $(0 , -4 )$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Focus: $(-1 , 3 )$; directrix $ 2x+3y=3$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Focus:$(2 , -3 );$ directrix :$2y-3=0$

asked Apr 9, 2013 by poojasapani_1

1 answer

If $ y = e^{\large a \: cos^{-1}x}, -1 \leq x \leq 1$, show that $(1- x^2)\large\frac{d^2y}{dx^2}-\normalsize x\large\frac{dy}{dx} -\normalsize a^2y \; = \; 0.$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $y = \begin{vmatrix} f(x) & g(x) & h(x) \\l & m &n \\ a & b & c \end{vmatrix}$, prove that $\large\frac{dy}{dx}\normalsize = \begin{vmatrix} f'(x) & g'(x) & h'(x) \\l & m &n \\ a & b & c \end{vmatrix}$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using the fact that $\sin (A + B) = \sin A \cos B + \cos A \sin B$ and the differentiation, obtain the sum formula for cosines.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using mathematical induction prove that $ \large\frac{d}{dx}\normalsize (x^{\large n}) = nx^{\large{n-1}} $ for all positive integers $n$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If $f (x) = |\; x\; |^3$, show that $f ″(x)$ exists for all real $x$ and find it.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If $x = a (\cos t + t\sin t)$ and $y = a (\sin t - t \cos\: t)$, find $ \large\frac{d^2y}{dx^2}$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If $cos\: y = x \cos (a + y)$, with $\cos$ $a \neq \pm 1$, prove that $ \large\frac{dy}{dx}=\frac{\cos^2(a + y)}{\sin \: a}$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Ask Questions, Get Answers

Find the equation of parabola if : Vertex $(1 , 4); $ open left ward and passing through the point $(-2,10)$

If a parabolic reflector is $20cm$ in diameter and $5cm$ deep, find the distance of the focus from the centre of the reflector.

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $x^{2}-6x-12y-3=0$.

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $y^{2}+8x-6y+1=0$.

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $(x-4)^{2}=4(y+2).$

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs.$x^{2}=20y $

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $y^{2}=-8x$

Find the equation of parabola if : Vertex $(2 , 3 )$ open upward ;and passing through the point $(6 , 4 )$.

Find the equation of parabola if :Vertex $(3 , -1 );$ open rightward ; the distance between the latus recturm and directrix is $4$.

Find the equation of parabola if : Vertex $(3 , -2 ); $ open downward and the length of the latus rectum is $8$.

Find the equation of parabola if : Vertex $(1 , 2 ) ;$ latus recturm :$y=5$.

Find the equation of parabola if : Vertex $(1 , 4 );$ focus :$(-2 , 4 ).$

Find the equation of parabola if : Vertex $(0 , 0 ); $ focus : $(0 , -4 )$.

Find the equation of parabola if : Focus: $(-1 , 3 )$; directrix $ 2x+3y=3$.

Find the equation of parabola if : Focus:$(2 , -3 );$ directrix :$2y-3=0$

If \( y = e^{\large a \: cos^{-1}x}, -1 \leq x \leq 1\), show that \((1- x^2)\large\frac{d^2y}{dx^2}-\normalsize x\large\frac{dy}{dx} -\normalsize a^2y \; = \; 0.\)

If \(y = \begin{vmatrix} f(x) & g(x) & h(x) \\l & m &n \\ a & b & c \end{vmatrix}\), prove that \(\large\frac{dy}{dx}\normalsize = \begin{vmatrix} f'(x) & g'(x) & h'(x) \\l & m &n \\ a & b & c \end{vmatrix}\)

Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

Using the fact that \(\sin (A + B) = \sin A \cos B + \cos A \sin B\) and the differentiation, obtain the sum formula for cosines.

Using mathematical induction prove that \( \large\frac{d}{dx}\normalsize (x^{\large n}) = nx^{\large{n-1}} \) for all positive integers \(n\).

If \(f (x) = |\; x\; |^3\), show that \(f ″(x)\) exists for all real \(x\) and find it.

If \(x = a (\cos t + t\sin t)\) and \(y = a (\sin t - t \cos\: t)\), find \( \large\frac{d^2y}{dx^2}\)

If \(cos\: y = x \cos (a + y)\), with $\cos$ \(a \neq \pm 1\), prove that \( \large\frac{dy}{dx}=\frac{\cos^2(a + y)}{\sin \: a}\)