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GradeEquation of a Parabola

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The least integral value of $k$ for which $\left( {k - 2} \right){x^2} + 8x + k + 4 > 0$ for all $x \in R$, is

A.5

B.4

C.3

D.None of these

A.5

B.4

C.3

D.None of these

Find the equation of parabola with vertex (0, 0) and focus at (0, 2).

Find the equation of parabola whose vertex is (0,0) and passing through (5,2) and symmetric with respect to y axis.

Prove that two parabolas, having the same focus and their axes in opposite directions, cut at right angles.

A quadrilateral is inscribed in a parabola ${{y}^{2}}=4ax$ and three of its sides pass through fixed points on the axis. Show that the fourth side also passes through a fixed point on the axis of the parabola.

The equation of the line joining the vertex of the parabola ${y^2} = 6x$ to the points on it whose abscissa is 24, is:

a. $y \pm 2x = 0$

b. $2y \pm x = 0$

c. $x \pm 2y = 0$

d. $2x \pm y = 0$

Equation of parabola with its vertex at \[(1,1)\] and focus \[(3,1)\] is

1) \[{(x - 1)^2} = 8(y - 1)\]

2) \[{(y - 1)^2} = 8(x - 3)\]

3) \[{(y - 1)^2} = 8(x - 1)\]

4) \[{(x - 3)^2} = 8(y - 1)\]

1) \[{(x - 1)^2} = 8(y - 1)\]

2) \[{(y - 1)^2} = 8(x - 3)\]

3) \[{(y - 1)^2} = 8(x - 1)\]

4) \[{(x - 3)^2} = 8(y - 1)\]

What is the equation of the parabola which has a vertex at the origin with a focus at \[\left( 5,0 \right)\]?

What is the equation of parabola with a vertex at $ \left( {2,3} \right) $ and focus at $ \left( {6,3} \right) $ ?

How do you find the equation for the parabola with the vertex $\left( 1,4 \right)$ that passes through the point $\left( 3,8 \right)$?

The cable of a uniformly loaded suspension bridge hangs in the form of parabola. The roadway which is horizontal and $ 100m $ long is supported by vertical wires attached to the cable, the longest wire being $ 30m $ and the shortest wire being $ 6m $ . Find the length of a supporting wire attached to the roadway $ 18m $ from the middle.

The vertex of a parabola is $\left( a,0 \right)$ and the directrix is $x+y=3a.$ The equation of the parabola is

$\left( a \right) {{x}^{2}}-2xy+{{y}^{2}}+6ax+10ay-7{{a}^{2}}=0$

$\left( b \right) {{x}^{2}}+2xy+{{y}^{2}}+6ax+10ay+2{{a}^{2}}=0$

$\left( c \right) {{x}^{2}}+2xy+{{y}^{2}}+6ax+10ay=2{{a}^{2}}$

$\left( d \right)$ None of these

$\left( a \right) {{x}^{2}}-2xy+{{y}^{2}}+6ax+10ay-7{{a}^{2}}=0$

$\left( b \right) {{x}^{2}}+2xy+{{y}^{2}}+6ax+10ay+2{{a}^{2}}=0$

$\left( c \right) {{x}^{2}}+2xy+{{y}^{2}}+6ax+10ay=2{{a}^{2}}$

$\left( d \right)$ None of these

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