AP EAPCET 2025 - 21st May Morning Shift | Straight Lines and Pair of Straight Lines Question 51 | Mathematics

If the slope of both the line given by $x^2+2 h x y+6 y^2=0$ are options and the angle between these lines is $\tan ^{-1}\left(\frac{1}{7}\right)$, then the product of the perpendiculars draw from the point $(1,0)$ to the given pair of lines is

$\frac{1}{6}$

$\frac{1}{5 \sqrt{2}}$

$\frac{5}{6}$

$\frac{1}{3 \sqrt{2}}$

AP EAPCET 2025 - 21st May Morning Shift

MCQ (Single Correct Answer)

-0

If one of the lines represented by $a x^2+2 h x y+b y^2=0$ bisects the angle between the positive coordinates axes, then

$a+b=2 h$

$a-b=2 h$

$a+2 h+b=0$

$a+2 h-b=0$

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

-0

The locus of the mid-point of the portion of the line $x \cos \alpha+y \sin \alpha=p$ intercepted by the coordinate axes, where $p$ is a constant, is

$\frac{1}{x^2}+\frac{1}{y^2}=\frac{3}{p^2}$

$\frac{1}{x^2}+\frac{1}{y^2}=\frac{4}{p^2}$

$x^2+y^2=2 p^2$

$\frac{2}{x^2}+\frac{2}{y^2}=\frac{1}{p^2}$

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

-0

The origin is shifted to the point $(2,3)$ by translation of axes and then the coordinate axes are rotated about the origin through an angle $\theta$ in the counter - clockwise sense. Due to this if the equation $3 x^2+2 x y+3 y^2-18 x-22 y+50=0$ is transformed to $4 x^2+2 y^2-1=0$, then the angle $\theta$ is euqal to

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{6}$

$\frac{\pi}{2}$

PREVIOUS NEXT

AP EAPCET Subjects

Browse all chapters by subject