Advertisements
Advertisements
प्रश्न
Write the value of \[\frac{dy}{dx}\] , if the normal to the curve y = f(x) at (x, y) is parallel to y-axis ?
Advertisements
उत्तर
The slope of the y-axis is \[\infty\].
Also, the normal at (x, y) on the curve y = f(x) is parallel to the y-axis.
∴ Slope of the normal =Slope of the y-axis = \[\infty\] \[\Rightarrow\frac{dy}{dx}=\text { Slope of the tangent }=\frac{- 1}{\text { Slope of the normal }}=\frac{- 1}{\infty}=0\]
APPEARS IN
संबंधित प्रश्न
Find the equation of the normal at a point on the curve x2 = 4y which passes through the point (1, 2). Also find the equation of the corresponding tangent.
Find the slope of the tangent to the curve y = x3 − 3x + 2 at the point whose x-coordinate is 3.
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x3 at (1, 1)
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x2 at (0, 0)
Find the points on the curve y = x3 at which the slope of the tangent is equal to the y-coordinate of the point.
Find the slope of the tangent and the normal to the following curve at the indicted point x = a cos3 θ, y = a sin3 θ at θ = π/4 ?
Find the slope of the tangent and the normal to the following curve at the indicted point y = (sin 2x + cot x + 2)2 at x = π/2 ?
Find the values of a and b if the slope of the tangent to the curve xy + ax + by = 2 at (1, 1) is 2 ?
If the tangent to the curve y = x3 + ax + b at (1, − 6) is parallel to the line x − y + 5 = 0, find a and b ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = x2 + 4x + 1 at x = 3 ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { at } \left( x_1 , y_1 \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point x2 = 4y at (2, 1) ?
Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is parallel to the line 2x − y + 9 = 0 ?
Find the equation of the tangent to the curve \[y = \sqrt{3x - 2}\] which is parallel to the 4x − 2y + 5 = 0 ?
Find the equation of the tangent to the curve x = sin 3t, y = cos 2t at
\[t = \frac{\pi}{4}\] ?
Find the angle of intersection of the following curve \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and x2 + y2 = ab ?
Find the angle of intersection of the following curve x2 + 4y2 = 8 and x2 − 2y2 = 2 ?
Find the angle of intersection of the following curve x2 + y2 = 2x and y2 = x ?
Show that the curves 4x = y2 and 4xy = k cut at right angles, if k2 = 512 ?
Prove that the curves y2 = 4x and x2 + y2 - 6x + 1 = 0 touch each other at the point (1, 2) ?
Write the angle between the curves y = e−x and y = ex at their point of intersections ?
The equation to the normal to the curve y = sin x at (0, 0) is ___________ .
The point on the curve y2 = x where tangent makes 45° angle with x-axis is ______________ .
The angle of intersection of the curves y = 2 sin2 x and y = cos 2 x at \[x = \frac{\pi}{6}\] is ____________ .
The point on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes is
(a) \[\left( 4, \frac{8}{3} \right)\]
(b) \[\left( - 4, \frac{8}{3} \right)\]
(c) \[\left( 4, - \frac{8}{3} \right)\]
(d) none of these
Find the angle of intersection of the curves y2 = 4ax and x2 = 4by.
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 = 2 ______.
Prove that the curves y2 = 4x and x2 + y2 – 6x + 1 = 0 touch each other at the point (1, 2)
The tangent to the curve y = e2x at the point (0, 1) meets x-axis at ______.
The slope of tangent to the curve x = t2 + 3t – 8, y = 2t2 – 2t – 5 at the point (2, –1) is ______.
The points on the curve `"x"^2/9 + "y"^2/16` = 1 at which the tangents are parallel to the y-axis are:
The tangent to the parabola x2 = 2y at the point (1, `1/2`) makes with the x-axis an angle of ____________.
The normal at the point (1, 1) on the curve `2y + x^2` = 3 is
The number of values of c such that the straight line 3x + 4y = c touches the curve `x^4/2` = x + y is ______.
The normals to the curve x = a(θ + sinθ), y = a(1 – cosθ) at the points θ = (2n + 1)π, n∈I are all ______.
If β is one of the angles between the normals to the ellipse, x2 + 3y2 = 9 at the points `(3cosθ, sqrt(3) sinθ)` and `(-3sinθ, sqrt(3) cos θ); θ ∈(0, π/2)`; then `(2 cot β)/(sin 2θ)` is equal to ______.
For the curve y2 = 2x3 – 7, the slope of the normal at (2, 3) is ______.
