If $a : b = 2 : 3$ and $b : c = 4 : 5$ is then $a^{2} : b^{2} : b c$ is

4 : 9 : 45

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16 : 36 : 20

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16 : 36 : 45

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45 : 36 : 20

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Solution

The correct option is C $16 : 36 : 45$
Given

$a : b = 2 : 3$ and $b : c = 4 : 5$

$\Rightarrow a = \frac{2}{3} b$ and $c = \frac{5}{4} b$

$\Rightarrow a^{2} = \frac{4}{9} b^{2}$ and $b c = \frac{5}{4} b^{2}$

$∴ a^{2} : b^{2} : b c = \frac{4}{9} : 1 : \frac{5}{4}$

$∴ a^{2} : b^{2} : b c = 16 : 36 : 45$

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Similar questions

∣ ∣ ∣ ∣ \begin{matrix} - 16 & 20 & 36 20 & - 25 & 45 36 & 45 & - 81 \end{matrix} ∣ ∣ ∣ ∣

Δ,

\sqrt{Δ}

Please let me know the mistake in this equation:

-20=-20

16-36=25-45

4²-4*9⁼5^2-5*9

4^{2 -}2*4* 9/2=5²-2*5* 9/2

(4-9/2)²= (5-9/2)²

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a : b = 2 : 3

b : c = 4 : 5

a^{2} : b^{2} : b c

Equation of the hyperbola with length of the latusrectum $\frac{9}{2}$ and e = $\frac{5}{4}$ is

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