TS EAMCET 2023 (Online) 12th May Evening Shift | Straight Lines and Pair of Straight Lines Question 27 | Mathematics

A line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the coordinate axes are rotated through an angle $\alpha$ and keeping the origin fixed, the same line $L$ has intercepts $p$ and $q$ on the new axes. Then,

$a^2+b^2=p^2+q^2$

$a^2+p^2=b^2+q^2$

$\frac{1}{a^2}+\frac{1}{p^2}=\frac{1}{b^2}+\frac{1}{q^2}$

$\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{p^2}+\frac{1}{q^2}$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

Two lines $L_1$ and $L_2$ passing through the point $P(1,2)$ cut the line $x+y=4$ at a distance of $\frac{\sqrt{6}}{3}$ units from $P$. Then, the angles made by $L_1, L_2$ with positive $X$-axis are

$\frac{\pi}{3}, \frac{\pi}{6}$

$\frac{\pi}{8}, \frac{3 \pi}{8}$

$\frac{\pi}{12}, \frac{5 \pi}{12}$

$\frac{\pi}{4}, \frac{\pi}{8}$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

A pair of straight lines drawn though the origin forms. an isosceles triangle right angled at the origin with the line $2 x+3 y=6$. The area (in sq units) of the triangle, so formed is

$36 / 13$

$32 / 13$

$28 / 9$

$26 / 9$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

The equation of the straight line passing through the point $(3,2)$ and inclined at an angle of $60^{\circ}$ with the line $\sqrt{3} x+y=1$ is

$\sqrt{3} x+y-(2+3 \sqrt{3})=0$

$\sqrt{3} x-y+(2-3 \sqrt{3})=0$

$-\sqrt{3} x+y-(2-3 \sqrt{3})=0$

$-\sqrt{3} x+y+(2-3 \sqrt{3})=0$

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