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Equation of Family of Circles Passing through Two Points

In the given ...

Question

In the given figure, if $A_{1}$ is the area of the $Δ A O B$ and $A_{2}$ is the area of the parabolic region $A O B$ with $x -$ axis, then the ratio $\frac{A_{1}}{A_{2}}$ is equal to

\frac{1}{2}

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\frac{3}{2}

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\frac{3}{4}

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\frac{2}{3}

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Solution

The correct option is B $\frac{3}{2}$

Area of parabolic curve $= (1 - \frac{2}{3})$ of rectangular area formed by two vertices as $A, B$ and other two on $x -$ axis
$\Rightarrow A_{2} = \frac{1}{3} [A B \times A M]$ and
$A_{1} = \frac{1}{2} (A B \times A M)$
So, $\frac{A_{1}}{A_{2}} = \frac{3}{2}$

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In the given figure, if A1 is the area of the ΔAOB and A2 is the area of the parabolic region AOB with x−axis, then the ratio A1 A2 is equal to

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In the given figure, if $A_{1}$ is the area of the $Δ A O B$ and $A_{2}$ is the area of the parabolic region $A O B$ with $x -$ axis, then the ratio $\frac{A_{1}}{A_{2}}$ is equal to

The correct option is B $\frac{3}{2}$

Area of parabolic curve $= (1 - \frac{2}{3})$ of rectangular area formed by two vertices as $A, B$ and other two on $x -$ axis
$\Rightarrow A_{2} = \frac{1}{3} [A B \times A M]$ and
$A_{1} = \frac{1}{2} (A B \times A M)$
So, $\frac{A_{1}}{A_{2}} = \frac{3}{2}$