Solve 1^2/4+y^2/9=1

$$\frac{ { 1 }^{ 2 } }{ 4 } + \frac{ { y }^{ 2 } }{ 9 } = 1$$

Solve for y

$$y = \frac{3 \sqrt{3}}{2} \approx 2.598076211$$

$$y = -\frac{3 \sqrt{3}}{2} \approx -2.598076211$$

Steps by Finding Square Root

Multiply both sides of the equation by 36, the least common multiple of 4,9.

$$9\times 1^{2}+4y^{2}=36$$

Calculate 1 to the power of 2 and get 1.

$$9\times 1+4y^{2}=36$$

Multiply 9 and 1 to get 9.

$$9+4y^{2}=36$$

Subtract 9 from both sides.

$$4y^{2}=36-9$$

Subtract 9 from 36 to get 27.

$$4y^{2}=27$$

Divide both sides by 4.

$$y^{2}=\frac{27}{4}$$

Take the square root of both sides of the equation.

$$y=\frac{3\sqrt{3}}{2} y=-\frac{3\sqrt{3}}{2}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 36, the least common multiple of 4,9.

$$9\times 1^{2}+4y^{2}=36$$

Calculate 1 to the power of 2 and get 1.

$$9\times 1+4y^{2}=36$$

Multiply 9 and 1 to get 9.

$$9+4y^{2}=36$$

Subtract 36 from both sides.

$$9+4y^{2}-36=0$$

Subtract 36 from 9 to get -27.

$$-27+4y^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$4y^{2}-27=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -27 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 4\left(-27\right)}}{2\times 4}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 4\left(-27\right)}}{2\times 4}$$

Multiply -4 times 4.

$$y=\frac{0±\sqrt{-16\left(-27\right)}}{2\times 4}$$

Multiply -16 times -27.

$$y=\frac{0±\sqrt{432}}{2\times 4}$$

Take the square root of 432.

$$y=\frac{0±12\sqrt{3}}{2\times 4}$$

Multiply 2 times 4.

$$y=\frac{0±12\sqrt{3}}{8}$$

Now solve the equation y=\frac{0±12\sqrt{3}}{8} when ± is plus.

$$y=\frac{3\sqrt{3}}{2}$$

Now solve the equation y=\frac{0±12\sqrt{3}}{8} when ± is minus.

$$y=-\frac{3\sqrt{3}}{2}$$

The equation is now solved.

$$y=\frac{3\sqrt{3}}{2} y=-\frac{3\sqrt{3}}{2}$$