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How do you find the intercepts of $x^{2} y - x^{2} + 4 y = 0$ ?

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(0,1)

(1,0)

(0,0)

(0,-1)

answer is C.

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Detailed Solution

The x-intercept is obtained by (a,0) and the y-intercept is given by (0,b).
For

x^{2} y - x^{2} + 4 y = 0

,
⇒

y = \frac{x^{2}}{x^{2} + 4}

In order to find the x-intercept, let's put

y = 0

and solve the equation accordingly.
⇒

0 = \frac{x^{2}}{x^{2} + 4}

⇒

x^{2} = 0

Taking square root,
⇒

x = 0

Hence, the x-intercept is equal to 0.
In order to find the y-intercept, let's put

x = 0

and solve the equation accordingly. Therefore, putting

x = 0

, we get
⇒

y = \frac{x^{2}}{x^{2} + 4}

⇒

y = \frac{0^{2}}{0^{2} + 4}

⇒

y = 0

Hence, the y-intercept is also equal to 0.

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