TG EAPCET 2024 (Online) 9th May Morning Shift | Straight Lines and Pair of Straight Lines Question 24 | Mathematics

$(a, b)$ is the point of concurrency of the lines $x-3 y+3=0, k x+y+k=0$ and $2 x+y-8=0$. If the perpendicular distance from the origin to the line $L=a x-b y+2 k=0$ is $p$, then the perpendicular distance from the point $(2,3)$ to $L=0$ is

$\frac{P}{2}$

$p$

$2 p$

$3 p$

TG EAPCET 2024 (Online) 9th May Morning Shift

MCQ (Single Correct Answer)

-0

If $(4,3)$ and $(1,-2)$ are the end points of a diagonal of a square, then the equation of one of its sides is

$4 x+y-11=0$

$2 x+y=0$

$2 x-3 y+1=0$

$x-4 y-9=0$

TG EAPCET 2024 (Online) 9th May Morning Shift

MCQ (Single Correct Answer)

-0

Area of the triangle bounded by the lines given by the equations $12 x^2-20 x y+7 y^2=0$ and $x+y-1=0$ is

$\frac{8}{29}$

$\frac{8}{39}$

$\frac{4}{29}$

$\frac{4}{39}$

TS EAMCET 2023 (Online) 12th May Evening Shift

MCQ (Single Correct Answer)

-0

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,

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

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

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

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

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