# Tutor profile: Seunggun L.

## Questions

### Subject: Korean

Describe your favorite KPOP song, in Korean! Write a short English translation as well.

저는 요즘 방탄소년단의 신곡 'Life Goes On'을 즐겨 들어요! 코로나 때문에 힘든 시기에 팬들에게 희망과 용기를 주기 위해 나온 곡이에요. 노래를 들으면 행복하고 힘이 나요! 방탄소년단 감사합니다~ These day's, I love listening to BTS's new song, 'Life Goes On'! The song came out to give the fans hope and courage, during this difficult pandemic. Listening to the song gives me joy and energy! Thank you so much, BTS~

### Subject: English

Please write a paragraph describing one way you destress during the Corona-19 pandemic.

Though I have always loved exercise during the pre-pandemic times, the virus has greatly impeded our ability to workout in close quarters. In an effort to maintain a healthy amount of movement, while also protecting myself and others from infection, I have begun hiking! Though masks are still on, hiking the beautiful mountains of South Korea has allowed me to destress in ways I've never imagined before. The fresh breeze, warm sunlight, beautiful leaves, and breath-taking views remind me that no matter how destitute things may seem, there is always wonder within the nature around us.

### Subject: Algebra

$$x^{2} + y^{2} - 10x - 4y = -20$$ The equation of a circle in the $$xy$$-plane is shown above. What is the radius of the circle? A) 2 B) 3 C) 7 D) 9

The answer is B. We use the standard form of the equation of a circle, which is $$(x-a)^{2} + (x-b)^{2} = c^{2}$$. $$(a,b)$$ is the center of the circle, and $$c$$ is the radius of the circle. We can now rewrite the given equation in the form of the standard equation to solve this problem: $$x^{2} + y^{2} - 10x - 4y = -20$$ We use the formula for quadratic equations with perfect squares: $$x^{2} - 2ax + a^{2} = (x-a)^{2}$$ Thus, we can rewrite the equation as such: $$(x^{2} - 10x + 25) -25 + (y^{2} - 4y + 4) -4 = -20$$ Notice how we offset the new integers $$+25$$ and $$+4$$ by negating them with $$-25$$ and $$-4$$. We convert the parentheses into squares: $$(x-5)^{2} -25 + (y-2)^{2} -4 = -20$$ We move the integers to the right: $$(x-5)^{2} + (y-2)^{2} = 9$$ Since 9 = $$3^{2}$$, we can rewrite the equation as such: $$(x-5)^{2} + (y-2)^{2} = 3^{2}$$ Referring to our standard form of the equation of a circle, we know that the radius is 3!