Question

* If the length of the tangent from (2,5) to the
circle x² + y2-54 +4y +K=0 is ,3

7 then find k.​

Answer 1

Step-by-step explanation:

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+k2=(5−0)2+(4+k)2

∴1+k2=25+k2+8k+16

∴8k+40=0

⇒k=−5