This is equation of a curve <msqrt> y </msqrt> + <msqrt> x </msqrt> =

enclinesbnnbk

enclinesbnnbk

Answered question

2022-05-15

This is equation of a curve y + x = A
A is a positive constant
T is a tangent of the curve from any point on it
B is the y-intercept of T
C is the x-intercept of T
Prove that B + C = A ..

Answer & Explanation

TettetoxDetnhte5

TettetoxDetnhte5

Beginner2022-05-16Added 15 answers

The tangent at the point ( x 0 , y 0 ) of the curve f ( x , y ) = 0 has equation
( x x 0 ) f x ( x 0 , y 0 ) + ( y y 0 ) f x = 0
and in this case we get
x x 0 2 x 0 ( + y y 0 2 y 0 ( = 0
Thus we can rewrite it as
x x 0 ( + y y 0 ( = A
or
x A x 0 ( + y A y 0 ( = 1
So the sum of the intercepts is
A ( x 0 ( + A ( y 0 ( = A
Jay Barrett

Jay Barrett

Beginner2022-05-17Added 2 answers

Assume a point ( h , k ) on the curve.
Differentiate given equation to get
y = y x
Therefore equation of tangent using slope point form is
y k = m ( x h ), where m is y
Put x = 0 , y = 0 for C and B, and then add the two

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