Advertisements
Advertisements
प्रश्न
Find the slope of the tangent and the normal to the following curve at the indicted point x2 + 3y + y2 = 5 at (1, 1) ?
उत्तर
\[x^2 + 3y + y^2 = 5\]
\[\text { On differentiating both sides w.r.t.x, we get }\]
\[2x + 3\frac{dy}{dx} + 2y \frac{dy}{dx} = 0\]
\[ \Rightarrow \frac{dy}{dx}\left( 3 + 2y \right) = - 2x\]
\[ \Rightarrow \frac{dy}{dx} = \frac{- 2x}{3 + 2y}\]
\[\text { Now,} \]
\[\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_\left( 1, 1 \right) =\frac{- 2x}{3 + 2y}=\frac{- 2}{3 + 2}=\frac{- 2}{5}\]
\[\text { Slope of the normal }=\frac{- 1}{\left( \frac{dy}{dx} \right)_\left( 1, 1 \right)}=\frac{- 1}{\left( \frac{- 2}{5} \right)}=\frac{5}{2}\]
APPEARS IN
संबंधित प्रश्न
Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is `6sqrt3` r.
Find the slope of the tangent to the curve y = 3x4 − 4x at x = 4.
Find points on the curve `x^2/9 + "y"^2/16 = 1` at which the tangent is parallel to x-axis.
Show that the tangents to the curve y = 7x3 + 11 at the points where x = 2 and x = −2 are parallel.
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 \[y = \sqrt{x} \text { at }x = 9\] ?
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 ?
At what points on the circle x2 + y2 − 2x − 4y + 1 = 0, the tangent is parallel to 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 \[\frac{x^2}{9} + \frac{y^2}{16} = 1\] at which the tangent is parallel to y-axis ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = x2 at (0, 0) ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = 2x2 − 3x − 1 at (1, −2) ?
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 \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { at } \left( x_1 , y_1 \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4ax at (x1, y1)?
Find the equation of the tangent and the normal to the following curve at the indicated points \[x = \frac{2 a t^2}{1 + t^2}, y = \frac{2 a t^3}{1 + t^2}\text { at } t = \frac{1}{2}\] ?
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 angle of intersection of the following curve y2 = x and x2 = y ?
If the tangent line at a point (x, y) on the curve y = f(x) is parallel to x-axis, then write the value of \[\frac{dy}{dx}\] ?
Write the value of \[\frac{dy}{dx}\] , if the normal to the curve y = f(x) at (x, y) is parallel to y-axis ?
Write the equation on the tangent to the curve y = x2 − x + 2 at the point where it crosses the y-axis ?
If the tangent to the curve x = a t2, y = 2 at is perpendicular to x-axis, then its point of contact 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 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 __________ .
Find the equation of tangent to the curve y = x2 +4x + 1 at (-1 , -2).
Find the angle of intersection of the curves y2 = x and x2 = y.
The point on the curve y2 = x, where the tangent makes an angle of `pi/4` with x-axis is ______.
The curve y = `x^(1/5)` has at (0, 0) ______.
The equation of normal to the curve 3x2 – y2 = 8 which is parallel to the line x + 3y = 8 is ______.
The equation of normal to the curve y = tanx at (0, 0) is ______.
The tangent to the parabola x2 = 2y at the point (1, `1/2`) makes with the x-axis an angle of ____________.
If `tan^-1x + tan^-1y + tan^-1z = pi/2`, then
Tangent is drawn to the ellipse `x^2/27 + y^2 = 1` at the point `(3sqrt(3) cos theta, sin theta), 0 < 0 < 1`. The sum of the intercepts on the axes made by the tangent is minimum if 0 is equal to
The number of common tangents to the circles x2 + y2 – 4x – 6x – 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 is
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.
The number of values of c such that the straight line 3x + 4y = c touches the curve `x^4/2` = x + y is ______.
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 ______.
