Advertisements
Advertisements
प्रश्न
Find the slope of the tangent to the curve y = (x -1)/(x - 2), x != 2 at x = 10.
Advertisements
उत्तर
APPEARS IN
संबंधित प्रश्न
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 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 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 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 = x2 where the slope of the tangent is equal to the x-coordinate of the point ?
At what point of the curve y = x2 does the tangent make an angle of 45° with the x-axis?
At what points on the curve y = 2x2 − x + 1 is the tangent parallel to the line y = 3x + 4?
At what points on the curve y = x2 − 4x + 5 is the tangent perpendicular to the line 2y + x = 7?
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 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 \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( x_0 , y_0 \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[x^\frac{2}{3} + y^\frac{2}{3}\] = 2 at (1, 1) ?
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 and the normal to the following curve at the indicated points x = a(θ + sinθ), y = a(1 − cosθ) at θ ?
The equation of the tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x − 5. Find the values of a and b ?
Find the equations of all lines of slope zero and that are tangent to the curve \[y = \frac{1}{x^2 - 2x + 3}\] ?
Find the equation of the tangent to the curve x2 + 3y − 3 = 0, which is parallel to the line y= 4x − 5 ?
Show that the following curve intersect orthogonally at the indicated point x2 = 4y and 4y + x2 = 8 at (2, 1) ?
Prove that the curves y2 = 4x and x2 + y2 - 6x + 1 = 0 touch each other at the point (1, 2) ?
If the straight line xcos \[\alpha\] +y sin \[\alpha\] = p touches the curve \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\] then prove that a2cos2 \[\alpha\] \[-\] b2sin2 \[\alpha\] = p2 ?
Write the angle between the curves y = e−x and y = ex at their point of intersections ?
Write the equation of the normal to the curve y = cos x at (0, 1) ?
The equation of the normal to the curve y = x + sin x cos x at x = `π/2` is ___________ .
The point at the curve y = 12x − x2 where the slope of the tangent is zero will be _____________ .
The angle of intersection of the curves xy = a2 and x2 − y2 = 2a2 is ______________ .
If the curve ay + x2 = 7 and x3 = y cut orthogonally at (1, 1), then a is equal to _____________ .
If the curves y = 2 ex and y = ae−x intersect orthogonally, then a = _____________ .
The normal at the point (1, 1) on the curve 2y + x2 = 3 is _____________ .
Find the equation of tangent to the curve y = x2 +4x + 1 at (-1 , -2).
The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is ______.
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.
The curve y = `x^(1/5)` has at (0, 0) ______.
Find points on the curve `x^2/9 + "y"^2/16` = 1 at which the tangent is parallel to y-axis.
Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is parallel to the line 2x − y + 9 = 0.
If `tan^-1x + tan^-1y + tan^-1z = pi/2`, then
The curve `(x/a)^n + (y/b)^n` = 2, touches the line `x/a + y/b` = 2 at the point (a, b) for n is equal to ______.
