Question

Number of circles touching all the lines
x+4y+1=0,2x+3y+3=0 and x -6y+3=0 is​

Answer 1

Answer:

one

Step-by-step explanation:

three equation form a triangle

Answer 2

Answer:

Number of circles touching the given lines is zero

Step-by-step explanation:

The given lines are

$x + 4y + 1 = 0 \\ 2x + 3y + 3 = 0 \\ x - 6y + 3 = 0$

First we check whether the lines are concurrent or not.For that we find the determinant of their coefficients as follows

$∆ = | 1&4&1 | \\ \: \: \: \: \: \: \: \: \: | 2&3&3 | \\ \: \: \: \: \: \: \: \: \: | 1&-6&3|$

$= 1(9 + 18) - 4(6 - 3) + 1( - 12 - 3) \\ = 27 - 12 - 15 = 0 \\ \\ = > ∆ = 0$

Since the determinant is zero,the lines are concurrent and intersect at a certain point.Hence,no circle can touch all the three lines.

Therefore,no.of circles touching the given lines is zero

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