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 ?
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 tangents to the curve y= x3 + 2x – 4, which are perpendicular to line x + 14y + 3 = 0.
Show that the equation of normal at any point t on the curve x = 3 cos t – cos3t and y = 3 sin t – sin3t is 4 (y cos3t – sin3t) = 3 sin 4t
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x4 − 6x3 + 13x2 − 10x + 5 at (1, 3)
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 equations of the tangent and normal to the hyperbola `x^2/a^2 - y^2/b^2` at the point `(x_0, y_0)`
The line y = x + 1 is a tangent to the curve y2 = 4x at the point
(A) (1, 2)
(B) (2, 1)
(C) (1, −2)
(D) (−1, 2)
The slope of the tangent to the curve x = t2 + 3t – 8, y = 2t2 – 2t – 5 at the point (2,– 1) is
(A) `22/7`
(B) `6/7`
(C) `7/6`
(D) `(-6)/7`
The line y = mx + 1 is a tangent to the curve y2 = 4x if the value of m is
(A) 1
(B) 2
(C) 3
(D) 1/2
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 ?
Find a point on the curve y = x3 − 3x where the tangent is parallel to the chord joining (1, −2) and (2, 2) ?
Find the points on the curve y2 = 2x3 at which the slope of the tangent is 3 ?
At what point of the curve y = x2 does the tangent make an angle of 45° with the x-axis?
Find the points on the curve y = 3x2 − 9x + 8 at which the tangents are equally inclined with the axes ?
Find the points on the curve \[\frac{x^2}{4} + \frac{y^2}{25} = 1\] at which the tangent is parallel to the x-axis ?
Find the points on the curve \[\frac{x^2}{9} + \frac{y^2}{16} = 1\] at which the tangent is parallel to x-axis ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[c^2 \left( x^2 + y^2 \right) = x^2 y^2 \text { at }\left( \frac{c}{\cos\theta}, \frac{c}{\sin\theta} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[x^\frac{2}{3} + y^\frac{2}{3}\] = 2 at (1, 1) ?
Find the equation of the tangent line to the curve y = x2 − 2x + 7 which perpendicular to the line 5y − 15x = 13. ?
Find the angle of intersection of the following curve x2 + y2 − 4x − 1 = 0 and x2 + y2 − 2y − 9 = 0 ?
Find the angle of intersection of the following curve x2 + 4y2 = 8 and x2 − 2y2 = 2 ?
Show that the following curve intersect orthogonally at the indicated point y2 = 8x and 2x2 + y2 = 10 at \[\left( 1, 2\sqrt{2} \right)\] ?
If the tangent to a curve at a point (x, y) is equally inclined to the coordinates axes then write the value of \[\frac{dy}{dx}\] ?
The point on the curve y2 = x where tangent makes 45° angle with x-axis is ______________ .
The point on the curve y = x2 − 3x + 2 where tangent is perpendicular to y = x is ________________ .
The point on the curve y = 6x − x2 at which the tangent to the curve is inclined at π/4 to the line x + y= 0 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 equation of the tangent line to the curve `"y" = sqrt(5"x" -3) -5`, which is parallel to the line `4"x" - 2"y" + 5 = 0`.
The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is ______.
Find the condition that the curves 2x = y2 and 2xy = k intersect orthogonally.
If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is ______.
The equation of tangent to the curve y(1 + x2) = 2 – x, where it crosses x-axis is ______.
Tangents to the curve x2 + y2 = 2 at the points (1, 1) and (-1, 1) are ____________.
Find points on the curve `x^2/9 + "y"^2/16` = 1 at which the tangent is parallel to y-axis.
Find the points on the curve `y = x^3` at which the slope of the tangent is equal to the y-coordinate of the point
An edge of variable cube is increasing at the rate of 3 cm/s. The volume of the cube increasing fast when the edge is 10 cm long is ______ cm3/s.
Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, From this horizontal plane is ______.
If m be the slope of a tangent to the curve e2y = 1 + 4x2, then ______.
