Advertisements
Advertisements
प्रश्न
Find the equation of the normal to curve y2 = 4x at the point (1, 2).
Advertisements
उत्तर
The equation of the given curve is y2 = 4x.
Differentiating with respect to x, we have:
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.
Find the equation of tangents to the curve y= x3 + 2x – 4, which are perpendicular to line x + 14y + 3 = 0.
Find the slope of the tangent to the curve y = 3x4 − 4x at x = 4.
Find the slope of the tangent to curve y = x3 − x + 1 at the point whose x-coordinate is 2.
Find the equations of all lines having slope 0 which are tangent to the curve y = `1/(x^2-2x + 3)`
Find points on the curve `x^2/9 + "y"^2/16 = 1` at which the tangent is parallel to x-axis.
The slope of the normal to the curve y = 2x2 + 3 sin x at x = 0 is
(A) 3
(B) 1/3
(C) −3
(D) `-1/3`
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 values of a and b if the slope of the tangent to the curve xy + ax + by = 2 at (1, 1) is 2 ?
If the tangent to the curve y = x3 + ax + b at (1, − 6) is parallel to the line x − y + 5 = 0, find a and b ?
Find the points on the curve y2 = 2x3 at which the slope of the tangent is 3 ?
At what point of the curve y = x2 does the tangent make an angle of 45° with the x-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 y = x2 + 4x + 1 at x = 3 ?
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 point \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { at } \left( x_1 , y_1 \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4x at (1, 2) ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( \sqrt{2}a, b \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated points x = θ + sinθ, y = 1 + cosθ at θ = \[\frac{\pi}{2}\] ?
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 ?
Show that the following set of curve intersect orthogonally x2 + 4y2 = 8 and x2 − 2y2 = 4 ?
Show that the curves 2x = y2 and 2xy = k cut at right angles, if k2 = 8 ?
Write the coordinates of the point on the curve y2 = x where the tangent line makes an angle \[\frac{\pi}{4}\] with x-axis ?
The equation to the normal to the curve y = sin x at (0, 0) is ___________ .
The equation of the normal to the curve 3x2 − y2 = 8 which is parallel to x + 3y = 8 is ____________ .
The angle of intersection of the curves xy = a2 and x2 − y2 = 2a2 is ______________ .
The line y = mx + 1 is a tangent to the curve y2 = 4x, if the value of m is ________________ .
Find the angle of intersection of the curves \[y^2 = 4ax \text { and } x^2 = 4by\] .
The equation of the normal to the curve y = sinx at (0, 0) is ______.
The point on the curve y2 = x, where the tangent makes an angle of `pi/4` with x-axis is ______.
Prove that the curves xy = 4 and x2 + y2 = 8 touch each other.
If the straight line x cosα + y sinα = p touches the curve `x^2/"a"^2 + y^2/"b"^2` = 1, then prove that a2 cos2α + b2 sin2α = p2.
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 – 2 = 0 intersect at an angle of ______.
At (0, 0) the curve y = x3 + x
The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan `"t"/2`)} at the point ‘t’ is ____________.
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).
The slope of the tangentto the curve `x= t^2 + 3t - 8, y = 2t^2 - 2t - 5` at the point `(2, -1)` is
