Home
Class 12
MATHS
Find the maximum number of points of int...

Find the maximum number of points of intersection of 7 straight lines and 5 circles when 3 straight lines are parallel and 2 circles are concentric

Text Solution

Verified by Experts

Points of intersection of 7 straight lines `= .^(7)C_(2)- .^(3)C_(2)=18`
Two concentric circles can intersect these 7 lines at maximum
=14+14=28 points
Third circle can intersect the given system at maximum
=14+2+2=18
Fourth circle can intersect the system at maximum
=14+2+2+2=20 points
Fifth circle can intersect the system at maximum
=14+2+2+2+2=22 points
`therefore` Maximum number of points of intersection
=18+28+18+20+22=106.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the maximum number of points of intersection of 6 circles.

Find the number of point of intersection of two straight lines .

The intersection of two straight lines gives us………

The maximum number of points of intersection of five lines and four circles is (A) 60 (B) 72 (C) 62 (D) none of these

Find the value of k, if the following equation represents a pair of straight lines . Further find wheter these lines are parallel or intersecting 12x^(2) + 7xy - 12 y^(2) - x + 7y + k = 0

Find the value of k if the following equation represents a pair of straight lines. Further, find whether these lines are parallel or intersecting 12x^(2)+7xy-12y^(2)-x+7y+k=0 .

Consider the curve y = x^(2) and the straight line y = 2x + 3 . (i) Find the points of intersection of the given curve and the straight line. (ii) Find the area of the region bounded by the given curve and the straight line.

Statement 1 : The equation x^2+y^2-2x-2a y-8=0 represents, for different values of a , a system of circles passing through two fixed points lying on the x-axis. Statement 2 : S=0 is a circle and L=0 is a straight line. Then S+lambdaL=0 represents the family of circles passing through the points of intersection of the circle and the straight line (where lambda is an arbitrary parameter).

A straight line that touches a circle at a common point is called a ___.