If the line passing through the point (- 1,0) is tangent to the circle x + y + 4x-2y + 3 = 0, then the intercept of the line on the Y axis is?

If the line passing through the point (- 1,0) is tangent to the circle x + y + 4x-2y + 3 = 0, then the intercept of the line on the Y axis is?

The point (- 1,0) is on the circle and has only one tangent
(x+2)^2+(y-1)^2=2
Center (- 2,1), radius = root 2
tangent
y=k(x+1)
kx-y+k=0
The distance from the center of the circle to the tangent is equal to the radius
So | - 2k-1 + K | / radical (k ^ 2 + 1) = radical 2
Square, finishing
(k+1)^2=2(k^2+1)
k^2+2k+1=2k^2+2
k^2-2k+1=0
k=1
x-y+1=0
y=x+1
So the intercept on the y-axis is 1

If the line passing through the point P (- 1, O) is tangent to the circle x ^ 2 + y ^ 2 + 4x-2y + 3 = 0, then the intercept of the line and the y-axis

x^2+y^2+4x-2y+3=0
(x+2)^2+(y-1)^2=2
Let this line be: y = K (x + 1)
|k(-2+1)-1|/√(1+k^2)=√2
(k+1)^2=2(1+k^2)
k^2+1-2k=0
(k-1)^2=0
k=1
So, the tangent equation is y = x + 1
The intercept between this line and Y axis is: 1