The line $L_1:y-x=0$and $L_2:2x+y=0$intersect the line $L_3:y+2=0$at P and Q respectively. The bisector of the acute angle between $L_1$and $L_2$intersects $L_3$at R.Statement-1 : The ratio $PR:RQ$equals $2\sqrt{2}:\sqrt{5}$Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles. Statement-1 is true, Statement-2 is true ; Statement-2 is correct explanation for Statement-1 Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for Statement-1 Statement-1 is true, Statement-2 is false Statement-1 is false, Statement-2 is true

If the line $2x+y=k$passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is

Let P be the point on the parabola, $y^2=8x$which is at a minimum distance from the centre C of the circle,$x^2+{\left(y+6\right)}^2=1.$Then the equation of the circle, passing through C and having its centre at P is :

The centres of those circles which touch the circle, $x^2+y^2-8x-8y-4=0$, externally and also touch the x-axis, lie on :

The straight line through a fixed point (2,3) intersects the coordinate axes at distinct point P and Q. If O is the origin and the rectangle OPRQ is completed then the locus of R is

A line is perpendicular to the line $2x-3y+5=0$ and passes through the points $\left(15,\beta \right)$ and $\left(7,17\right)$ then value of $\beta$ will be equal to (A) $\frac{35}{3}$ (B) $-\frac{35}{3}$ (C) $5$ (D) $-5$

If S is a set of triangles whose one vertex is origin and other two vertices are integral coordinates and lies on coordinate axis of area 50 square units, then number of elements in set S is equal to (a) 9 (b) 18 (c) 36 (d) 40

A line passes through $\left(-3,4\right)$ and the portion of the line intercepted between the coordinate axes is bisected at the point then equation of line is (A) $4x-3y+24=0$ (B) $x-y-7=0$ (C) $3x-4y+25=0$ (D) $3x-4y+24=0$

A point P moves on line $2x-3y+4=0$ If $Q\left(1,4\right)$ and $R\left(3,-2\right)$ are fixed points, then the locus of the centroid of $△PQR$ is a line: (a) with slope $\frac{3}{2}$ (b) parallel to y-axis (c) with slope $\frac{2}{3}$ (d) parallel to x-axis