HARD
JEE Main/Advanced
IMPORTANT
Earn 100

Find equations of the sides of the triangle having 3,-1 as a vertex, x-4y+10=0 and 6 x+10y-59=0 being the equation of an angle bisector and a median respectively drawn from different vertices.

Important Questions on The Straight Lines

EASY
JEE Main/Advanced
IMPORTANT
The line joining Abcosα,bsinα and Bacosβ,asinβ is produced to the point Mx,y so that AM and BM are in the ratio b:a. Then prove that x+ytanα+β2=0.  
HARD
JEE Main/Advanced
IMPORTANT

The base BC of a triangle ABC contains the points Pp1,q1 and Qp2,q2 and the equation of sides AB and AC are p1x+q1y=1 and q2x+p2y=1 respectively. Prove that the equations of AP and AQ are

p1q2+q1p2-1p1x+q1y-1=p12+q12-1q2x+p2y-1

and 2p2q2-1p1x+q1y-1=p1p2+q1q2-1q2x+p2y-1 respectively.

HARD
JEE Main/Advanced
IMPORTANT
The points 1,3 and5,1  are two opposite vertices of a rectangle. The other two vertices lie on the line y=2x+c. Find c and the remaining vertices.
HARD
JEE Main/Advanced
IMPORTANT
Equations of two straight lines are xcosα+ysinα=p and xcosβ+ysinβ=p'. Show that the area of the quadrilateral formed by the two lines and the perpendiculars drawn from the origin to the lines is 12sinβ-α2pp'-p2+p'2cosα-β.
HARD
JEE Main/Advanced
IMPORTANT
One diagonal of a square is the portion of the line 7 x+5y=35 intercepted by the axes. Obtain the extremities of the other diagonal.
MEDIUM
JEE Main/Advanced
IMPORTANT
A ray of light is sent along the line x-2y+5=0, upon reaching 3x-2y+7=0 the ray is reflected back from it. Find the equation of lines containing the reflected ray.
HARD
JEE Main/Advanced
IMPORTANT
Show that the reflection of the line px+qy+r=0 in the line x+y+1=0 is the line qx+py+p+q-r=0, where p-q.
HARD
JEE Main/Advanced
IMPORTANT
If bases and the sum of area of a number of triangles have a common vertex, then show that the locus of this vertex is a straight line.