If the length of the intercept made on the li | vedclass

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(D) The point of intersection of lines $y=ax$ and $y=2$ is $A\left(\frac{2}{a}, 2\right)$.The point of intersection of lines $y=ax$ and $y=6$ is $B\le

Vedclass · Accepted Answer

$a  \frac{4}{3}$

Vedclass · Answer

(D) The point of intersection of lines $y=ax$ and $y=2$ is $A\left(\frac{2}{a}, 2\right)$.The point of intersection of lines $y=ax$ and $y=6$ is $B\left(\frac{6}{a}, 6\right)$.The length of the segment $AB$ is given by the distance formula:$AB = \sqrt{\left(\frac{6}{a} - \frac{2}{a}\right)^2 + (6 - 2)^2} $\sqrt{\left(\frac{4}{a}\right)^2 + 4^2} $\sqrt{\frac{16}{a^2} + 16} Squaring both sides:$\frac{16}{a^2} + 16 $\frac{16}{a^2} $a^2 > \frac{16}{9}$Taking the square root,we get $|a| > \frac{4}{3}$,which implies $a  \frac{4}{3}$.Thus,option $D$ is correct.

If the length of the intercept made on the line $y=ax$ by the lines $y=2$ and $y=6$ is less than $5$,then which of the following is true?

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