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Points Y and Z are points of tangency. Find the value of a.

Points Y And Z Are Points Of Tangency Find The Value Of A class=

Sagot :

Gmanyidn

Answer:

a = 2

Step-by-step explanation:

If Y and Z are points of tangency, then |XY| = |XZ|.

We have

[tex]|XY|=9a^2-30\\|XZ|=3a[/tex]

Domain

[tex]a>0[/tex]

Substitute

[tex]9a^2-30=3a\qquad|\text{subtract}\ 3a\ \text{from both sides}\\\\9a^2-3a-30=0\qquad|\text{divide both sides by 3}\\\\3a^2-a-10=0\\\\3a^2-6a+5a-10=0\\\\3a(a-2)+5(a-2)=0\\\\(a-2)(3a+5)=0\iff a-2=0\ \vee\ 3a+5=0\\\\a-2=0\qquad|\text{add 2 to both sides}\\a=2\\\\3a+5=0\qquad|\text{subtract 5 from both sides}\\3a=-5\qquad|\text{divide both sides by 3}\\a=-\dfrac{5}{3}<0[/tex]

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