Advertisements
Advertisements
प्रश्न
Write the equation of the normal to the curve y = cos x at (0, 1) ?
Advertisements
उत्तर
\[\text { Given }: \]
\[y = \cos x\]
\[\text { On differentiating both sides w.r.t.x, we get }\]
\[\frac{dy}{dx} = - \sin x\]
\[\text { Now }, \]
\[\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_\left( 0, 1 \right) =-sin 0=0\]
\[\text { and }\]
\[\text { Equation of the normal }\]
\[ = y - y_1 = \frac{- 1}{m}\left( x - x_1 \right)\]
\[ \Rightarrow y - 1 = \frac{- 1}{0}\left( x - 0 \right)\]
\[ \Rightarrow x = 0\]
APPEARS IN
संबंधित प्रश्न
Find the equations of the tangent and normal to the curve x = a sin3θ and y = a cos3θ at θ=π/4.
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 equation of all lines having slope 2 which are tangents to the curve `y = 1/(x- 3), x != 3`
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x2 at (0, 0)
Find the equations of the tangent and normal to the given curves at the indicated points:
x = cos t, y = sin t at t = `pi/4`
Find the equation of the normal at the point (am2, am3) for the curve ay2 = x3.
Find the equation of the normals to the curve y = x3 + 2x + 6 which are parallel to the line x + 14y + 4 = 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)
Find the equation of the normal to curve y2 = 4x at the point (1, 2).
Find the slope of the tangent and the normal to the following curve at the indicted point x = a (θ − sin θ), y = a(1 − cos θ) at θ = −π/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 points on the curve y = x3 − 2x2 − 2x at which the tangent lines are parallel to the line y = 2x− 3 ?
Find the point on the curve y = 3x2 + 4 at which the tangent is perpendicular to the line whose slop is \[- \frac{1}{6}\] ?
Find the points on the curve\[\frac{x^2}{4} + \frac{y^2}{25} = 1\] at which the tangent is parallel to the y-axis ?
Find the equation of the tangent to the curve \[\sqrt{x} + \sqrt{y} = a\] at the point \[\left( \frac{a^2}{4}, \frac{a^2}{4} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( x_0 , y_0 \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( \sqrt{2}a, b \right)\] ?
Find the equation of a normal to the curve y = x loge x which is parallel to the line 2x − 2y + 3 = 0 ?
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 tangents to the curve 3x2 – y2 = 8, which passes through the point (4/3, 0) ?
Show that the following curve intersect orthogonally at the indicated point x2 = 4y and 4y + x2 = 8 at (2, 1) ?
Show that the curves 2x = y2 and 2xy = k cut at right angles, if k2 = 8 ?
Find the point on the curve y = x2 − 2x + 3, where the tangent is parallel to x-axis ?
Write the coordinates of the point at which the tangent to the curve y = 2x2 − x + 1 is parallel to the line y = 3x + 9 ?
The point on the curve y2 = x where tangent makes 45° angle with x-axis is ______________ .
The slope of the tangent to the curve x = t2 + 3 t − 8, y = 2t2 − 2t − 5 at point (2, −1) is ________________ .
The equation of the normal to the curve x = a cos3 θ, y = a sin3 θ at the point θ = π/4 is __________ .
The angle of intersection of the parabolas y2 = 4 ax and x2 = 4ay at the origin is ____________ .
Find the condition for the curves `x^2/"a"^2 - y^2/"b"^2` = 1; xy = c2 to interest orthogonally.
Find the angle of intersection of the curves y2 = 4ax and x2 = 4by.
The point on the curve y2 = x, where the tangent makes an angle of `pi/4` with x-axis is ______.
Find an angle θ, 0 < θ < `pi/2`, which increases twice as fast as its sine.
Find the condition that the curves 2x = y2 and 2xy = k intersect orthogonally.
The equation of tangent to the curve y(1 + x2) = 2 – x, where it crosses x-axis is ______.
The points on the curve `"x"^2/9 + "y"^2/16` = 1 at which the tangents are parallel to the y-axis are:
For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?
The tangent to the curve y = x2 + 3x will pass through the point (0, -9) if it is drawn at the point ____________.
The number of values of c such that the straight line 3x + 4y = c touches the curve `x^4/2` = x + y is ______.
Find the equation to the tangent at (0, 0) on the curve y = 4x2 – 2x3
