Answer:
y = 2[tex]\sqrt{5}[/tex]
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
Here r = 6 [ (0, 0 ) → (6, 0 ) ⇒ r = 6 ]
Since Q lies on the circle then it satisfies the equation
Q = (4, y )
Substitute (4, y ) and r = 6 into the equation
4² + y² = 6²
16 + y² = 36 ( subtract 16 from both sides )
y² = 20 ( take square root of both sides )
y = [tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]
Q = 4, 2[tex]\sqrt{5}[/tex] )
