Advertisements
Advertisements
प्रश्न
The point on the curve y2 = x, where the tangent makes an angle of `pi/4` with x-axis is ______.
विकल्प
`(1/2, 1/4)`
`(1/4, 1/2)`
(4, 2)
(1, 1)
Advertisements
उत्तर
The point on the curve y2 = x, where the tangent makes an angle of `pi/4` with x-axis is `(1/4, 1/2)`.
Explanation:
`"dy"/"dx" = 1/(2y) = tan pi/4` = 1
⇒ y = `1/2`
⇒ x = `1/4`
APPEARS IN
संबंधित प्रश्न
Find the equations of the tangent and normal to the curve x = a sin3θ and y = a cos3θ at θ=π/4.
The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b.
Find the slope of the tangent to the curve y = x3 − 3x + 2 at the point whose x-coordinate is 3.
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x2 at (0, 0)
For the curve y = 4x3 − 2x5, find all the points at which the tangents passes through the origin.
Find the slope of the tangent and the normal to the following curve at the indicted point \[y = \sqrt{x^3} \text { at } x = 4\] ?
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 y = 2x2 + 3 sin x at x = 0 ?
Find the slope of the tangent and the normal to the following curve at the indicted point xy = 6 at (1, 6) ?
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 points on the curve y = 2x2 − x + 1 is the tangent parallel to the line y = 3x + 4?
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 to the curve \[\sqrt{x} + \sqrt{y} = a\] at the point \[\left( \frac{a^2}{4}, \frac{a^2}{4} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4x at (1, 2) ?
Find the equations of all lines having slope 2 and that are tangent to the curve \[y = \frac{1}{x - 3}, x \neq 3\] ?
Find the angle of intersection of the following curve x2 + y2 − 4x − 1 = 0 and x2 + y2 − 2y − 9 = 0 ?
Show that the following set of curve intersect orthogonally x2 + 4y2 = 8 and x2 − 2y2 = 4 ?
Show that the following curve intersect orthogonally at the indicated point x2 = 4y and 4y + x2 = 8 at (2, 1) ?
Show that the following curve intersect orthogonally at the indicated point y2 = 8x and 2x2 + y2 = 10 at \[\left( 1, 2\sqrt{2} \right)\] ?
If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of \[\frac{dx}{dy}\] ?
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 y = e−x and y = ex at their point of intersections ?
The equation to the normal to the curve y = sin x at (0, 0) is ___________ .
The point at the curve y = 12x − x2 where the slope of the tangent is zero will be _____________ .
If the line y = x touches the curve y = x2 + bx + c at a point (1, 1) then _____________ .
The curves y = aex and y = be−x cut orthogonally, if ___________ .
Find the angle of intersection of the curves y2 = x and x2 = y.
Prove that the curves xy = 4 and x2 + y2 = 8 touch each other.
Find the co-ordinates of the point on the curve `sqrt(x) + sqrt(y)` = 4 at which tangent is equally inclined to the axes
If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is ______.
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 – 2 = 0 intersect at an angle of ______.
The points on the curve `"x"^2/9 + "y"^2/16` = 1 at which the tangents are parallel to the y-axis are:
`"sin"^"p" theta "cos"^"q" theta` attains a maximum, when `theta` = ____________.
The normal at the point (1, 1) on the curve `2y + x^2` = 3 is
If the curves y2 = 6x, 9x2 + by2 = 16, cut each other at right angles then the value of b is ______.
The number of values of c such that the straight line 3x + 4y = c touches the curve `x^4/2` = x + y is ______.
If m be the slope of a tangent to the curve e2y = 1 + 4x2, then ______.
