Home
Class 11
MATHS
If the equation of any two diagonals ...

If the equation of any two diagonals of a regular pentagon belongs to the family of lines `(1+2lambda)lambda-(2+lambda)x+1-lambda=0` and their lengths are sin `36^0` , then the locus of the center of circle circumscribing the given pentagon (the triangles formed by these diagonals with the sides of pentagon have no side common) is (a) `x^2+y^2-2x-2y+1+sin^2 72^0=0` (b)`x^2+y^2-2x-2y+cos^2 72^0=0` (c)`x^2+y^2-2x-2y+1+cos^2 72^0=0` (d)`x^2+y^2-2x-2y+sin^2 72^0=0`

Promotional Banner

Similar Questions

Explore conceptually related problems

Length of the shortest chord of the parabola y^(2)=4x+8, which belongs to the family of lines (1+lambda)y+(lambda-1)x+2(1-lambda)=0 is

If the family of lines lambda x+3y-6=0(lambda is variable) intersect the lines x-2y+3=0 and x-y+1=0 in P and Q,then locus of the middle point of PQ is

If the following equations x+y-3=0,(1+lambda)x+(2+lambda)y-8=0,x-(1+lambda)y+(2+lambda)=0 are consistent then the value of lambda is

2x^(2)+2y^(2)+4 lambda x+lambda=0 represents a circle for

For any lambda in R, the locus x^(2)+y^(2)-2 lambda x-2 lambda y+lambda^(2)=0 touches the line

2x^(2)+2y^(2)+2 lambda x+lambda^(2)=0 represents a circle for

The locus of the mid-point of a chord of the circle x^2 + y^2 -2x - 2y - 23=0 , of length 8 units is : (A) x^2 + y^2 - x - y + 1 =0 (B) x^2 + y^2 - 2x - 2y - 7 = 0 (C) x^2 + y^2 - 2x - 2y + 1 = 0 (D) x^2 + y^2 + 2x + 2y + 5 = 0

The centre of family of circles cutting the family of circles x^(2)+y^(2)+4x(lambda-(3)/(2))+3y(lambda-(4)/(3))-6(lambda+2)=0 orthogonally,lies on

Equation (2 + lambda)x^2-2 lambdaxy+(lambda -1)y^2-4x-2=0 represents a hyperbola if