Question

Which of the following points lies on the circle whose center is at the origin and whose radius is 10?

Answer 1

The equation is: $\frac{(x - 0)^{2} }{10^{2} } + \frac{(y - 0)^{2} }{10^{2} } = 1$

= $\frac{x^{2} }{10^{2} } + \frac{y^{2} }{10^{2} } = 1$

A) $\frac{(\sqrt{10}) ^{2} }{10^{2} } + \frac{(0)^{2} }{10^{2} } = 1$

⇒ $\frac{10}{100}$ + 0 = 1   FALSE

B) $\frac{(0) ^{2} }{10^{2} } + \frac{(2\sqrt{5})^{2} }{10^{2} } = 1$

⇒ 0 + $\frac{20}{100}$ = 1   FALSE

C) $\frac{(5\sqrt{2}) ^{2} }{10^{2} } + \frac{(5\sqrt{2})^{2} }{10^{2} } = 1$

⇒ $\frac{50}{100}$ + $\frac{50}{100}$ = 1   TRUE

Answer: C