Advertisements
Advertisements
प्रश्न
Find the equation of the normal at the point (am2, am3) for the curve ay2 = x3.
Advertisements
उत्तर
The equation of the given curve is ay2 = x3.
On differentiating with respect to x, we have:
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 the slope of the tangent to curve y = x3 − x + 1 at the point whose x-coordinate is 2.
Find points at which the tangent to the curve y = x3 − 3x2 − 9x + 7 is parallel to the x-axis.
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 equation of all lines having slope −1 that are tangents to the curve `y = 1/(x -1), x != 1`
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x3 at (1, 1)
Find the points on the curve y = `4x^3 - 3x + 5` at which the equation of the tangent is parallel to the x-axis.
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 ?
Find the point on the curve y = 3x2 + 4 at which the tangent is perpendicular to the line whose slop is \[- \frac{1}{6}\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4ax at \[\left( \frac{a}{m^2}, \frac{2a}{m} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated points x = asect, y = btant at t ?
Find the equation of the tangent line to the curve y = x2 − 2x + 7 which perpendicular to the line 5y − 15x = 13. ?
Find the equation of the tangent to the curve \[y = \sqrt{3x - 2}\] which is parallel to the 4x − 2y + 5 = 0 ?
Prove that the curves y2 = 4x and x2 + y2 - 6x + 1 = 0 touch each other at the point (1, 2) ?
Find the condition for the following set of curve to intersect orthogonally \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { and } \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1\] ?
If the tangent to a curve at a point (x, y) is equally inclined to the coordinates axes then write the value of \[\frac{dy}{dx}\] ?
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 angle between the curves y2 = 4x and x2 = 2y − 3 at the point (1, 2) ?
The equation of the normal to the curve y = x(2 − x) at the point (2, 0) is ________________ .
The point on the curve y2 = x where tangent makes 45° angle with x-axis is ______________ .
If the tangent to the curve x = a t2, y = 2 at is perpendicular to x-axis, then its point of contact 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 __________ .
The angle of intersection of the curves y = 2 sin2 x and y = cos 2 x at \[x = \frac{\pi}{6}\] is ____________ .
The normal at the point (1, 1) on the curve 2y + x2 = 3 is _____________ .
The normal to the curve x2 = 4y passing through (1, 2) is _____________ .
Find the condition for the curves `x^2/"a"^2 - y^2/"b"^2` = 1; xy = c2 to interest orthogonally.
Find the angle of intersection of the curves y2 = 4ax and x2 = 4by.
The tangent to the curve given by x = et . cost, y = et . sint at t = `pi/4` makes with x-axis an angle ______.
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 points at which the tangents to the curve y = x3 – 12x + 18 are parallel to x-axis are ______.
The slope of tangent to the curve x = t2 + 3t – 8, y = 2t2 – 2t – 5 at the point (2, –1) is ______.
For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?
The tangent to the parabola x2 = 2y at the point (1, `1/2`) makes with the x-axis an angle of ____________.
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:
Let `y = f(x)` be the equation of the curve, then equation of normal is
The normal at the point (1, 1) on the curve `2y + x^2` = 3 is
If (a, b), (c, d) are points on the curve 9y2 = x3 where the normal makes equal intercepts on the axes, then the value of a + b + c + d is ______.
If the curves y2 = 6x, 9x2 + by2 = 16, cut each other at right angles then the value of b is ______.
