help@askiitians.com

+91-87964 74404

Grade 11Analytical Geometry

The lines joining the origin to the point of intersection of 3x^2+lambda xy -4x+1=0 and 2x+y-1=0 are at right angles for
Lambda= A.-4, B.4 , C.7 D.No value of lamda

Trisanu Bhar

8 Years agoGrade 11

1 Answer

Nishant Vora

Approved Tutor Answer8 Years ago

Here we have to use the concept of homoginization

2x + y =1 is the given line.

$3x^2+\lambda xy -4x(2x + y)+1(2x + y)^2=0$
$3x^2+\lambda xy -8x^2 - 4xy + 4x^2 + y^2 + 4xy = 0$
Now apply a + b = 0 as agle is 90 deg

$3x^2+\lambda xy -8x^2 - 4xy + 4x^2 + y^2 + 4xy = 0$
$-x^2+\lambda xy + y^2= 0$

So answer should be all values of lambda

The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d

analytical geometry

1 Answer Available

Last Activity: 4 Years ago

View all Questions