The slope of the tangent to a curve at any point (x, y) on the curve is negative 1 times x divided by y. Find the equation of the curve if the point (3, −4) is on the curve.

Question

The slope of the tangent to a curve at any point (x, y) on the curve is . Find the equation of the curve if the point (3, −4) is on the curve.

 x + y = −1 

x² + y² = 5 

x² + y² = 25

 x² − y² = −7

Answer 1

dy/dx = -x/y

y dy = -x dx

x² + y² = C

9 + 16 = 25

therefore x² + y² = 25