Question

/2) of the length of the tangent
from (5, 4) to the circle
x² + y²+2ky=0 is 1 , then find k​

Answer 1

Answer:

The radius of the circle, the tangent from (5,4) and the point (5,4) when joined to the center of the circle, (0,−k) forms a right angled triangle.

∴ (length of tangent)^2 + (radius)^2 = (distance of (5,4) from center of the circle)^2

∴ (length of tangent)^2+k^2 =(5−0)^2 +(4+k) ^2

∴1+k^2 =25+k^2+8k+16

∴8k+40=0

⇒k=−5