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# hlp plz

-1
120
3

https://vle.mathswatch.co.uk/images/questions/question16855.png

Jun 29, 2020

#1
+8352
0

If the line is tangent to the circle, then the line and the circle only touch at one point. That means if I solve for x( or y), there should only be one solution.

$$\begin{cases}x = 2y + 5\\x^2 + y^2 = 5\end{cases}$$

Substituting the first equation into the second,

$$(2y + 5)^2 + y^2 = 5\\ 4y^2 + 20y + 25 + y^2 = 5\\ 5y^2 + 20y + 20 = 0\\ y^2 + 4y + 4 = 0\\ (y + 2)^2 = 0\\ \boxed{y = -2}$$

As you see, it only has one solution. Therefore the line is indeed tangent to the circle.

Jun 29, 2020
#2
0

i got 4/5 i am confused

Guest Jun 29, 2020
#3
+8352
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Can you show me what you did to get 4/5?

MaxWong  Jun 29, 2020