Advertisements
Advertisements
प्रश्न
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 \[\frac{dy}{dx}\] ?
उत्तर
The slope of the x-axis is 0.
Also, the tangent at a point (x, y) on the curve y = f(x) is parallel to the x-axis.
∴ Slope of the tangent
\[\left( \frac{dy}{dx} \right)\] = Slope of the x-axis = 0.
APPEARS IN
संबंधित प्रश्न
Find a point on the curve y = (x − 2)2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x4 − 6x3 + 13x2 − 10x + 5 at (1, 3)
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 equations of the tangent and the normal, to the curve 16x2 + 9y2 = 145 at the point (x1, y1), where x1 = 2 and y1 > 0.
Find the slope of the tangent and the normal to the following curve at the indicted point y = x3 − x at x = 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 ?
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 point on the curve y = x2 where the slope of the tangent is equal to the x-coordinate of the point ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = x4 − bx3 + 13x2 − 10x + 5 at (0, 5) ?
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 normal to the curve ay2 = x3 at the point (am2, am3) ?
Determine the equation(s) of tangent (s) line to the curve y = 4x3 − 3x + 5 which are perpendicular to the line 9y + x + 3 = 0 ?
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 angle of intersection of the following curve y = x2 and x2 + y2 = 20 ?
Find the angle of intersection of the following curve 2y2 = x3 and y2 = 32x ?
Find the angle of intersection of the following curve x2 + y2 − 4x − 1 = 0 and x2 + y2 − 2y − 9 = 0 ?
Find the angle of intersection of the following curve x2 = 27y and y2 = 8x ?
Show that the following set of curve intersect orthogonally x3 − 3xy2 = −2 and 3x2y − y3 = 2 ?
Prove that the curves y2 = 4x and x2 + y2 - 6x + 1 = 0 touch each other at the point (1, 2) ?
The angle between the curves y2 = x and x2 = y at (1, 1) is ______________ .
The curves y = aex and y = be−x cut orthogonally, if ___________ .
The equation of the normal to the curve x = a cos3 θ, y = a sin3 θ at the point θ = π/4 is __________ .
If the curves y = 2 ex and y = ae−x intersect orthogonally, then a = _____________ .
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 angle of intersection of the curves y = 2 sin2 x and y = cos 2 x at \[x = \frac{\pi}{6}\] is ____________ .
Any tangent to the curve y = 2x7 + 3x + 5 __________________ .
The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is ______.
Prove that the curves xy = 4 and x2 + y2 = 8 touch each other.
Prove that the curves y2 = 4x and x2 + y2 – 6x + 1 = 0 touch each other at the point (1, 2)
Show that the line `x/"a" + y/"b"` = 1, touches the curve y = b · e– x/a at the point where the curve intersects the axis of y
The equation of normal to the curve 3x2 – y2 = 8 which is parallel to the line x + 3y = 8 is ______.
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 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:
If the curves y2 = 6x, 9x2 + by2 = 16, cut each other at right angles then the value of b is ______.
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 ______.
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 ______.
For the curve y2 = 2x3 – 7, the slope of the normal at (2, 3) is ______.
