Advertisements
Advertisements
प्रश्न
Write the equation of the normal to the curve y = cos x at (0, 1) ?
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 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.
The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b.
Find the slope of the tangent to curve y = x3 − x + 1 at the point whose x-coordinate is 2.
Find the equations of all lines having slope 0 which are tangent to the curve y = `1/(x^2-2x + 3)`
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x4 − 6x3 + 13x2 − 10x + 5 at (0, 5)
Show that the tangents to the curve y = 7x3 + 11 at the points where x = 2 and x = −2 are parallel.
Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis.
Find the equation of the tangent to the curve `y = sqrt(3x-2)` which is parallel to the line 4x − 2y + 5 = 0.
Find the equation of the normal to curve y2 = 4x at the point (1, 2).
Find a point on the curve y = x3 − 3x where the tangent is parallel to the chord joining (1, −2) and (2, 2) ?
At what points on the circle x2 + y2 − 2x − 4y + 1 = 0, the tangent is parallel to x-axis?
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 2a2y = x3 − 3ax2 where the tangent is parallel to 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 points on the curve \[\frac{x^2}{9} + \frac{y^2}{16} = 1\] at which the tangent is parallel to y-axis ?
Who that the tangents to the curve y = 7x3 + 11 at the points x = 2 and x = −2 are parallel ?
Find the equation of the tangent and the normal to the following curve at the indicated point\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text{ at }\left( a\cos\theta, b\sin\theta \right)\] ?
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 the normal to the curve ay2 = x3 at the point (am2, am3) ?
Find the angle of intersection of the following curve y = x2 and x2 + y2 = 20 ?
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 y = 4 − x2 and y = x2 ?
Show that the following set of curve intersect orthogonally y = x3 and 6y = 7 − x2 ?
Show that the following set of curve intersect orthogonally x2 + 4y2 = 8 and x2 − 2y2 = 4 ?
Write the angle made by the tangent to the curve x = et cos t, y = et sin t at \[t = \frac{\pi}{4}\] with the x-axis ?
The equation of the normal to the curve y = x(2 − x) at the point (2, 0) is ________________ .
The point on the curve y = x2 − 3x + 2 where tangent is perpendicular to y = x is ________________ .
The slope of the tangent to the curve x = t2 + 3 t − 8, y = 2t2 − 2t − 5 at point (2, −1) is ________________ .
The curves y = aex and y = be−x cut orthogonally, if ___________ .
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 line y = mx + 1 is a tangent to the curve y2 = 4x, if the value of m is ________________ .
The normal at the point (1, 1) on the curve 2y + x2 = 3 is _____________ .
Find the angle of intersection of the curves y2 = 4ax and x2 = 4by.
Prove that the curves y2 = 4x and x2 + y2 – 6x + 1 = 0 touch each other at the point (1, 2)
If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is ______.
If the curves y2 = 6x, 9x2 + by2 = 16, cut each other at right angles then the value of b is ______.
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 ______.
If the tangent to the conic, y – 6 = x2 at (2, 10) touches the circle, x2 + y2 + 8x – 2y = k (for some fixed k) at a point (α, β); then (α, β) is ______.
