Question

the number of circles touching all the three lines 2x+y=3,4x-y=3,x+y=2 is​

Answer 1

Answer:

Hope this will help you

Answer 2

Given:

Equation 1 = L1 = 2x+y=3

Equation 2 = L2 = 4x-y=3

Equation 3 = L3 = x+y=2

To find:

Number of circles touching all three lines

Solution:

L1 + L2

= 2x+y=3 + 4x-y=3

= 6x = 6

Thus, x = 1 and y = 1

(1,1)

Similarly,

L2 and L3

4x-y=3 + x+y=2

5x = 5

Thus, x = 1 and y = 1

(1,1)

Similarly for L3 and L1

x = 1 and y = 1

(1,1)

On plotting the values on the x-axis and y-axis, the chord will intersect at one point.

Answer: the number of circles touching all the three lines is Zero

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