Home
Class 12
MATHS
Two circles passing through A(1,2), B(2...

Two circles passing through `A(1,2), B(2,1)` touch the line `4x + 8y-7 = 0` at C and D such that ACED in a parallelogram. Then:

Text Solution

AI Generated Solution

To solve the problem step by step, we will follow the reasoning provided in the video transcript. ### Step 1: Identify Points and Parallelogram Properties We have two points A(1, 2) and B(2, 1). We need to find point E and C such that A, C, E, D form a parallelogram. ### Step 2: Midpoint of Diagonal In a parallelogram, the diagonals bisect each other. Therefore, the midpoint of AC must be equal to the midpoint of ED. Let point E be (H, K). The midpoint of AC is given by: \[ ...
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE ENGLISH|Exercise Examples|13 Videos

  • CIRCLE

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 4.1|1 Videos

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise Matrix|4 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

Two circles C_1a n dC_2 both pass through the points A(1,2)a n dE(2,1) and touch the line 4x-2y=9 at B and D , respectively. The possible coordinates of a point C , such that the quadrilateral A B C D is a parallelogram, are (a ,b)dot Then the value of |a b| is_________

The circle passing through (1, -2) and touching the axis of x at (3, 0) also passes through the point

Find the equation of the circle passing through (-1,0) and touching x+ y-7 = 0 at (3,4)

A circle passes through (0,0) and (1, 0) and touches the circle x^2 + y^2 = 9 then the centre of circle is -

a circle passing through the point (2,2(sqrt2-1)) touches the pair of lines x^2 -y^2 -4x+4 =0 . The centre of the circle is

lf a circle C passing through (4,0) touches the circle x^2 + y^2 + 4x-6y-12 = 0 externally at a point (1, -1), then the radius of the circle C is :-

The circle passing through the point (-1,0) and touching the y-axis at (0,2) also passes through the point:

The centre of the circle passing through the points (0,0), (1,0) and touching the circle x^2+y^2=9 is

A circle having centre at C is made to pass through the point P(1,2), touching the straight lines 7x-y=5 and x+y+13=0 at A and B respectively. Then

A circle passes through point (3, sqrt(7/2)) and touches the line-pair x^2 - y^2 - 2x +1 = 0 . Centre of circle lies inside the circle x^2 + y^2 - 8x + 10y + 15 = 0 . Coordinates of centre of circle are given by