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

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

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

Mathematics
Equation of a parabola
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.
Mathematics
Equation of a 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. $2x \pm y = 0$

Mathematics
Equation of a parabola
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) ${(x - 3)^2} = 8(y - 1)$
Mathematics
Equation of a parabola
What is the equation of the parabola which has a vertex at the origin with a focus at $\left( 5,0 \right)$?

Mathematics
Equation of a parabola
What is the equation of parabola with a vertex at $\left( {2,3} \right)$ and focus at $\left( {6,3} \right)$ ?
Mathematics
Equation of a parabola
How do you find the equation for the parabola with the vertex $\left( 1,4 \right)$ that passes through the point $\left( 3,8 \right)$?

Mathematics
Equation of a parabola
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.
Mathematics
Equation of a parabola
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
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