मराठी

Find the Equation of the Normal to Curve Y2 = 4x at the Point (1, 2). - Mathematics

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:

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Application of Derivatives - Exercise 6.6 [पृष्ठ २४२]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 6 Application of Derivatives
Exercise 6.6 | Q 4 | पृष्ठ २४२

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Find the equation of tangents to the curve y= x3 + 2x – 4, which are perpendicular to line x + 14y + 3 = 0.


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 point on the curve y = x3 − 11x + 5 at which the tangent is y = x − 11.

 

Find the equation of all lines having slope 2 which are tangents to the curve `y =   1/(x- 3), x != 3`


Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is perpendicular to the line 5y − 15x = 13.


Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis.


Prove that the curves x = y2 and xy = k cut at right angles if 8k2 = 1. [Hint: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]


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 ?


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 xy + 4 = 0 at which the tangents are inclined at an angle of 45° with the x-axis ?


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 x2 + y2 = 13, the tangent at each one of which is parallel to the line 2x + 3y = 7 ?


Find the equation of the normal to y = 2x3 − x2 + 3 at (1, 4) ?


Find the equation of the tangent and the normal to the following curve at the indicated point\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text{ at }\left( a\cos\theta, b\sin\theta \right)\] ?


Find the equation of the tangent and the normal to the following curve at the indicated point  \[x^\frac{2}{3} + y^\frac{2}{3}\] = 2 at (1, 1) ?


Find the equation of the tangent and the normal to the following curve at the indicated points x = at2, y = 2at at t = 1 ?


Find the equation of the normal to the curve ay2 = x3 at the point (am2, am3) ?


Find the equation of the tangent to the curve x = sin 3ty = cos 2t at

\[t = \frac{\pi}{4}\] ?


Find the angle of intersection of the following curve y2 = x and x2 = y  ?


Find the angle of intersection of the following curve  x2 + 4y2 = 8 and x2 − 2y2 = 2 ?


Find the angle of intersection of the following curve x2 + y2 = 2x and y2 = x ?


Show that the following set of curve intersect orthogonally x2 + 4y2 = 8 and x2 − 2y2 = 4 ?


Find the slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at t = 2 ?


The point on the curve y = x2 − 3x + 2 where tangent is perpendicular to y = x is ________________ .


The slope of the tangent to the curve x = t2 + 3 t − 8, y = 2t2 − 2t − 5 at point (2, −1) is ________________ .


The slope of the tangent to the curve x = 3t2 + 1, y = t3 −1 at x = 1 is ___________ .


If the curves y = 2 ex and y = ae−x intersect orthogonally, then a = _____________ .


The slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at the point (2, −1) is _____________ .


Find the equation of a tangent and the normal to the curve `"y" = (("x" - 7))/(("x"-2)("x"-3)` at the point where it cuts the x-axis


Find the angle of intersection of the curves y2 = x and x2 = y.


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 ______.


Find the equation of the normal lines to the curve 3x2 – y2 = 8 which are parallel to the line x + 3y = 4.


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 equation of normal to the curve 3x2 – y2 = 8 which is parallel to the line x + 3y = 8 is ______.


The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 – 2 = 0 intersect at an angle of ______.


The number of common tangents to the circles x2 + y2 – 4x – 6x – 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 is


Let `y = f(x)` be the equation of the curve, then equation of normal is


The line is y = x + 1 is a tangent to the curve y2 = 4x at the point.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×