2) One of the roots of equation y? - 4y + k = 0 is 2 - V7. Find the value of y.
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Answer:
The straight line 3x+4y−k=0 touches the circle x
2
−16x+y
2
=0
The perpendicular distance between the line and the centre of the circle equals the radius.
The centre of the circle is (8,0) and the radius is
64+0−0
=8
⇒
∣
∣
∣
∣
∣
∣
3
2
+4
2
24−k
∣
∣
∣
∣
∣
∣
=8
⇒∣24−k∣=40
⇒24−k=±40
⇒k=−16,64
Step-by-step explanation:
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