New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Straight Lines and Pair of Straight Lines question

2022 · 28 Jun · Shift 1 · Q39

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Straight Lines and Pair of Straight Lines
2022 · 28 Jun · Shift 1 · Q39

Straight Lines and Pair of Straight Lines question

2022 · 28 Jun · Shift 1 · Q39

JEE MainMathematicsStraight Lines and Pair of Straight LinesNumerical+4 / −1

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be (

\alpha

,

\beta

). Then, the value of 7

\alpha

+ 3

\beta

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Straight Lines and Pair of Straight Lines

Let a triangle be bounded by the lines L1 : 2x + 5y = 10; L2 : $-$ 4x + 3y = 12 and the line L3, which passes through the point P(2, 3), intersects L2 at A and L1 at B. If the point P divides the line-segment AB, internally in the ratio 1…2022 · MCQ
Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP intersects the line BC at the point Q $(k_{1}, k_{2})$ , then $k_{1} + k_{2}$ is equal to :2022 · MCQ
Let $m_{1}, m_{2}$ be the slopes of two adjacent sides of a square of side a such that $a^{2} + 11 a + 3 (m_{1}^{2} + m_{2}^{2}) = 220$ . If one vertex of the square is $(10 (cos α - sin α), 10 (sin α + cos α))$ ,…2022 · MCQ
Let $A (α, - 2), B (α, 6)$ and $C (\frac{α}{4}, - 2)$ be vertices of a $△ ABC$ . If $(5, \frac{α}{4})$ is the circumcentre of $△ ABC$ , then…2022 · MCQ
The distance between the two points A and A' which lie on y = 2 such that both the line segments AB and A' B (where B is the point (2, 3)) subtend angle $\frac{π}{4}$ at the origin, is equal to :2022 · MCQ
The distance of the origin from the centroid of the triangle whose two sides have the equations $x - 2 y + 1 = 0$ and $2 x - y - 1 = 0$ and whose orthocenter is $(\frac{7}{3}, \frac{7}{3})$ is :2022 · MCQ
Let $α$ 1, $α$ 2 ( $α$ 1 2) be the values of $α$ fo the points ( $α$ , $-$ 3), (2, 0) and (1, $α$ ) to be collinear. Then the equation of the line, passing through ( $α$ 1, $α$ 2) and making an angle of $\frac{π}{3}$ …2022 · MCQ
Let the points of intersections of the lines x $-$ y + 1 = 0, x $-$ 2y + 3 = 0 and 2x $-$ 5y + 11 = 0 are the mid points of the sides of a triangle $Δ$ ABC. Then, the area of the $Δ$ ABC is .2021 · Numerical