Solve the formula $$\frac { x ^ { 2 } } { d ^ { 2 } } + \frac { y ^ { 2 } } { n ^ { 2 } } = 1 ; y$$
for the indicated variable.
A) $\quad y = \sqrt { n ( 2 - x d ) ( 1 + x d ) } , y = - \sqrt { n ( 2 - x d ) ( 1 + x d ) }$
B) $\quad y = \sqrt { n ( 1 - x d ) ( 1 + x d ) } , y = - \sqrt { n \left( 1 - x d ^ { d } \right) ( 1 + x d ) }$
C) $y = n \sqrt { \left( 1 - \frac { x } { d } \right) \left( 1 + \frac { x } { d } \right) } , y = - n \sqrt { \left( 1 - \frac { x } { d } \right) \left( 1 + \frac { x } { d } \right) }$
D)$y=\sqrt{n\left(1-\frac{x}{d}\right)^{2}}, y=-\sqrt{n\left(1-\frac{x}{d}\right)^{2}}$e.

E) $y=n \sqrt{\left(\mathrm{a}-\frac{x}{d}\right)\left(\mathrm{a}+\frac{x}{d}\right)}, y=-n \sqrt{\left(\mathrm{a}-\frac{x}{d}\right)\left(\mathrm{a}+\frac{x}{d}\right)}$

Question

Solve the formula $$\frac { x ^ { 2 } } { d ^ { 2 } } + \frac { y ^ { 2 } } { n ^ { 2 } } = 1 ; y$$
for the indicated variable.
A) $\quad y = \sqrt { n ( 2 - x d ) ( 1 + x d ) } , y = - \sqrt { n ( 2 - x d ) ( 1 + x d ) }$
B) $\quad y = \sqrt { n ( 1 - x d ) ( 1 + x d ) } , y = - \sqrt { n \left( 1 - x d ^ { d } \right) ( 1 + x d ) }$
C) $y = n \sqrt { \left( 1 - \frac { x } { d } \right) \left( 1 + \frac { x } { d } \right) } , y = - n \sqrt { \left( 1 - \frac { x } { d } \right) \left( 1 + \frac { x } { d } \right) }$
D)$y=\sqrt{n\left(1-\frac{x}{d}\right)^{2}}, y=-\sqrt{n\left(1-\frac{x}{d}\right)^{2}}$e.

E) $y=n \sqrt{\left(\mathrm{a}-\frac{x}{d}\right)\left(\mathrm{a}+\frac{x}{d}\right)}, y=-n \sqrt{\left(\mathrm{a}-\frac{x}{d}\right)\left(\mathrm{a}+\frac{x}{d}\right)}$

Quizplus · Accepted Answer

To solve for $y$, we rearrange the given equation: $\frac{x^2}{d^2} + \frac{y^2}{n^2} = 1$ to isolate $y^2$, giving $y^2 = n^2\left(1 - \frac{x^2}{d^2}\right)$. Factoring the expression inside the parentheses gives $y^2 = n^2\left(\left(1 - \frac{x}{d}\right)\left(1 + \frac{x}{d}\right)\right)$. Taking the square root of both sides gives two solutions for $y$: $y = n\sqrt{\left(1 - \frac{x}{d}\right)\left(1 + \frac{x}{d}\right)}$ and $y = -n\sqrt{\left(1 - \frac{x}{d}\right)\left(1 + \frac{x}{d}\right)}$, which matches choice C.

Solve the Formula x2d2+y2n2=1;y\frac { x ^ { 2 } } { d ^ { 2 } } + \frac { y ^ { 2 } } { n ^ { 2 } } = 1 ; yd2x2​+n2y2​=1;y

Solve the Formula $\frac { x ^ { 2 } } { d ^ { 2 } } + \frac { y ^ { 2 } } { n ^ { 2 } } = 1 ; y$