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Popular >

solvefor x,y=xsqrt(16-x^2)

Solution

solve for

x, y = x 16 - x^{2}

Solution

x = 8 - - y^{2} + 64 {0 \leq y \leq 8}, x = - 8 - - y^{2} + 64 {- 8 \leq y \leq 0}, x = - y^{2} + 64 + 8 {0 \leq y \leq 8}, x = - - y^{2} + 64 + 8 {- 8 \leq y \leq 0}

Solution steps

y = x 16 - x^{2}

Square both sides:

y^{2} = 16 x^{2} - x^{4}

y^{2} = 16 x^{2} - x^{4}

Solve

y^{2} = 16 x^{2} - x^{4} : x = 8 - - y^{2} + 64, x = - 8 - - y^{2} + 64, x = - y^{2} + 64 + 8, x = - - y^{2} + 64 + 8

x = 8 - - y^{2} + 64, x = - 8 - - y^{2} + 64, x = - y^{2} + 64 + 8, x = - - y^{2} + 64 + 8

Verify Solutions:

x = 8 - - y^{2} + 64 {0 \leq y \leq 8}, x = - 8 - - y^{2} + 64 {- 8 \leq y \leq 0}, x = - y^{2} + 64 + 8 {0 \leq y \leq 8}, x = - - y^{2} + 64 + 8 {- 8 \leq y \leq 0}

The solutions are

x = 8 - - y^{2} + 64 {0 \leq y \leq 8}, x = - 8 - - y^{2} + 64 {- 8 \leq y \leq 0}, x = - y^{2} + 64 + 8 {0 \leq y \leq 8}, x = - - y^{2} + 64 + 8 {- 8 \leq y \leq 0}

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