As per the given question,
Differentiate the following functions with respect to x: 
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Exercise 11.2
Differentiate the following functions with respect to x:
Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.
We realize that the vertex is \[\left( 0,\text{ }0 \right)\]and the hub of the parabola is the \[y-axis\] The condition of the parabola is both of the from \[{{x}^{2~}}=\text{ }4ay\text{ }or\text{...
Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis.
We realize that the vertex is \[\left( 0,\text{ }0 \right)\]and the hub of the parabola is the \[x-axis\] The condition of the parabola is both of the from \[~{{y}^{2~}}=\text{ }4ax\text{ }or\text{...
Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0); focus (–2, 0)
Given: \[Vertex\text{ }\left( 0,\text{ }0 \right)\text{ }and\text{ }focus\text{ }\left( -2,\text{ }0 \right)\] We realize that the vertex of the parabola is \[\left( 0,\text{ }0 \right)~\]and the...
Find the equation of the parabola that satisfies the given conditions: Vertex (0, 0); focus (3, 0)
Given: Vertex \[\left( 0,\text{ }0 \right)\]and concentration \[\left( 3,\text{ }0 \right)\] We realize that the vertex of the parabola is \[\left( 0,\text{ }0 \right)\]and the attention lies on the...
Find the equation of the parabola that satisfies the given conditions: Focus (0,–3); directrix y = 3
Given: \[Focus\text{ }\left( 0,\text{ }-3 \right)\text{ }and\text{ }directrix\text{ }y\text{ }=\text{ }3\] We realize that the emphasis lies on the \[y-axis\] is the axis of the parabola. Along...
Find the equation of the parabola that satisfies the given conditions: Focus (6,0); directrix x = – 6
Given: \[Focus\text{ }\left( 6,0 \right)\text{ }and\text{ }directrix\text{ }x\text{ }=\text{ }-6\] We realize that the emphasis lies on the \[xaxis\] is the axis of the parabola. Along these lines,...
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. x^2 = – 9y
Given: The condition is \[{{x}^{2}}~=\text{ }-9y\] Here we realize that the coefficient of \[y\]is negative . Along these lines, the parabola opens towards downwards . On contrasting this condition...
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. y^2 = 10x
Given: The condition is \[{{y}^{2}}~=\text{ }10x\]. Here we realize that the coefficient of \[x\text{ }is\text{ }positive\] . Along these lines, the parabola opens towards right . On contrasting...
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. x^2 = – 16y
Given: The condition is \[{{x}^{2}}~=\text{ }-16y\]. Here, we realize that the coefficient of \[y\] is negative. Along these lines, the parabola opens towards downwards . On contrasting this...
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. y^2 = – 8x
Given: The condition is \[{{y}^{2}}~=\text{ }-8x\] Here we realize that the coefficient of $x$ is negative. Along these lines, the parabola opens towards left. On contrasting this condition and...
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.x^2 = 6y
Given: The condition is \[{{x}^{2}}~=\text{ }6y\] Here we realize that the coefficient of $y$is positive . Along these lines, the parabola opens towards upwards . On contrasting this condition and...
Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. y^2 = 12x
Given: The condition is \[{{y}^{2}}~=\text{ }12x\] Here we realize that the coefficient of $x$is positive. Along these lines, the parabola opens towards right . On contrasting this condition and...