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
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.
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 curve `x^2/a^2−y^2/b^2=1` at the point `(sqrt2a,b)` .
Find the slope of the tangent to curve y = x3 − x + 1 at the point whose x-coordinate is 2.
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 = x3 at (1, 1)
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.
Find the slope of the tangent and the normal to the following curve at the indicted point \[y = \sqrt{x} \text { at }x = 9\] ?
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 = 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 equation of the tangent and the normal to the following curve at the indicated point xy = c2 at \[\left( ct, \frac{c}{t} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point x2 = 4y at (2, 1) ?
Find the equation of the tangent line to the curve y = x2 + 4x − 16 which is parallel to the line 3x − y + 1 = 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 ?
Prove that \[\left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2\] touches the straight line \[\frac{x}{a} + \frac{y}{b} = 2\] for all n ∈ N, at the point (a, b) ?
At what points will be tangents to the curve y = 2x3 − 15x2 + 36x − 21 be parallel to x-axis ? Also, find the equations of the tangents to the curve at these points ?
Show that the following set of curve intersect orthogonally y = x3 and 6y = 7 − x2 ?
Show that the curves 4x = y2 and 4xy = k cut at right angles, if k2 = 512 ?
Write the coordinates of the point on the curve y2 = x where the tangent line makes an angle \[\frac{\pi}{4}\] with x-axis ?
Write the equation on the tangent to the curve y = x2 − x + 2 at the point where it crosses the y-axis ?
The equation of the normal to the curve y = x + sin x cos x at x = `π/2` is ___________ .
The angle of intersection of the curves xy = a2 and x2 − y2 = 2a2 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 __________ .
Any tangent to the curve y = 2x7 + 3x + 5 __________________ .
Find the angle of intersection of the curves y2 = 4ax and x2 = 4by.
The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is ______.
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 = 2 ______.
The tangent to the curve given by x = et . cost, y = et . sint at t = `pi/4` makes with x-axis an angle ______.
Prove that the curves xy = 4 and x2 + y2 = 8 touch each other.
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:
Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is parallel to the line 2x − y + 9 = 0.
The number of common tangents to the circles x2 + y2 – 4x – 6x – 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 is
Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ, then a value of tan θ is:
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
The slope of the tangentto the curve `x= t^2 + 3t - 8, y = 2t^2 - 2t - 5` at the point `(2, -1)` is
