Advertisements
Advertisements
Question
Find the equation of tangent and normal to the following curve.
xy = c2 at `("ct", "c"/"t")` where t is parameter.
Solution
Equation of the curve is xy = c2
Differentiating w.r.t. x, we get
`"x" "dy"/"dx" + "y" = 0`
∴ `"dy"/"dx" = (- "y")/"x"`
∴ slope of tangent at `("ct", "c"/"t")` is
`("dy"/"dx")_(("ct", "c"/"t")` = `((- "c")/"t")/"ct" = (- 1)/"t"^2`
Equation of tangent at `("ct", "c"/"t")` is
`("y" - "c"/"t") = (-1)/"t"^2 ("x" - "ct")`
∴ yt2 - ct = - x + ct
∴ x + yt2 - 2ct = 0
Slope of normal =`(-1)/((-1)/"t"^2) = "t"^2`
Equation of normal at `("ct", "c"/"t")` is
`("y" - "c"/"t") = "t"^2 ("x" - "ct")`
∴ yt - c = xt3 - ct4
∴ t3x - yt - (t4 - 1)c = 0
Notes
The answer in the textbook is incorrect.
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following function from first principle.
x3 – 27
Find the derivative of the following function from first principle.
(x – 1) (x – 2)
Find the derivative of the following function from first principle:
sin (x + 1)
Find the derivative of the following function from first principle:
`cos (x - pi/8)`
Find the equation of tangent and normal to the curve at the given points on it.
y = 3x2 - x + 1 at (1, 3)
Find the equations of tangent and normal to the curve y = x2 + 5 where the tangent is parallel to the line 4x − y + 1 = 0.
Find the equations of tangent and normal to the curve y = 3x2 - 3x - 5 where the tangent is parallel to the line 3x − y + 1 = 0.
Choose the correct alternative.
The equation of tangent to the curve y = x2 + 4x + 1 at (-1, -2) is
Choose the correct alternative.
If elasticity of demand η = 1, then demand is
Choose the correct alternative.
If 0 < η < 1, then demand is
Fill in the blank:
The slope of tangent at any point (a, b) is called as _______.
Find the equation of tangent and normal to the following curve.
x = `1/"t", "y" = "t" - 1/"t"`, at t = 2
Find the equation of tangent and normal to the following curve.
y = x3 - x2 - 1 at the point whose abscissa is -2.
Find the equation of normal to the curve y = `sqrt(x - 3)` which is perpendicular to the line 6x + 3y – 4 = 0.
The slope of the tangent to the curve y = x3 – x2 – 1 at the point whose abscissa is – 2, is ______.
Find the equation of tangent to the curve x2 + y2 = 5, where the tangent is parallel to the line 2x – y + 1 = 0
Find the equation of tangent and normal to the curve y = x2 + 5 where the tangent is parallel to the line 4x – y + 1 = 0.
