TS EAMCET 2023 (Online) 12th May Evening Shift | Straight Lines and Pair of Straight Lines Question 32 | Mathematics

If $\theta$ is the acute angle between the lines joining the origin to the points of intersection of the curve $x^2+x y+y^2+x+3 y+1=0$ and the straight line $x+y+2=0$, then $\cos \theta=$

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

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

$\frac{3}{5}$

$\frac{4}{5}$

TS EAMCET 2023 (Online) 12th May Morning Shift

MCQ (Single Correct Answer)

-0

The angle, by which the coordinate axes are to be rotated about the origin so that the transformed equation of $\sqrt{3} x^2+(\sqrt{3}-1) x y-y^2=0$ would be free from $x y$-term is

$45^{\circ}$

$22.5^{\circ}$

$15^{\circ}$

$7.5^{\circ}$

TS EAMCET 2023 (Online) 12th May Morning Shift

MCQ (Single Correct Answer)

-0

If the slope of a straight line passing through $A(3,2)$ is $3 / 4$, then the coordinates of the two points on the same line that are 5 units away from $A$ are

$(-7,5),(1,-1)$

$(7,5),(-1,-1)$

$(6,9),(-2,3)$

$(6,3),(-2,-3)$

TS EAMCET 2023 (Online) 12th May Morning Shift

MCQ (Single Correct Answer)

-0

If each of the points $(a, 4),(-2, b)$ lies on the line joining the points $(2,-1)$ and $(5,-3)$, then the point $(a, b)$ lies on the line

$6 x+6 y-25=0$

$x+3 y+1=0$

$2 x+6 y+1=0$

$2 x+3 y-5=0$

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