मराठी

Find the Equation of the Normal at the Point (Am2, Am3) for the Curve Ay2 = X3. - Mathematics

Advertisements
Advertisements

प्रश्न

Find the equation of the normal at the point (am2am3) for the curve ay2 = x3.

उत्तर

The equation of the given curve is ay2 = x3.

On differentiating with respect to x, we have:

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 6: Application of Derivatives - Exercise 6.3 [पृष्ठ २१२]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
पाठ 6 Application of Derivatives
Exercise 6.3 | Q 20 | पृष्ठ २१२

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Find the slope of the tangent to the curve y = 3x4 − 4x at x = 4.


Find points at which the tangent to the curve y = x3 − 3x2 − 9x + 7 is parallel to the x-axis.


Find the equations of the tangent and normal to the given curves at the indicated points:

y = x3 at (1, 1)


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


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

(A) `22/7`

(B) `6/7`

(C) `7/6`

(D) `(-6)/7`


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  xy = 6 at (1, 6) ?


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 points on the curve y = x3 − 2x2 − 2x at which the tangent lines are parallel to the line y = 2x− 3 ?


Find the points on the curve y = x3 where the slope of the tangent is equal to the x-coordinate of the point ?


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 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 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  \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( a\sec\theta, b\tan\theta \right)\] ?


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 line to the curve y = x2 − 2x + 7 which is parallel to the line 2x − y + 9 = 0 ?


Show that the following set of curve intersect orthogonally y = x3 and 6y = 7 − x?


Show that the following curve intersect orthogonally at the indicated point y2 = 8x and 2x2 +  y2 = 10 at  \[\left( 1, 2\sqrt{2} \right)\] ?


Show that the curves 2x = y2 and 2xy = k cut at right angles, if k2 = 8 ?


If the straight line xcos \[\alpha\] +y sin \[\alpha\] = p touches the curve  \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\] then prove that a2cos2 \[\alpha\] \[-\] b2sin\[\alpha\] = p?


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 \[\frac{dy}{dx}\] ?


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 equation of the tangent drawn to the curve \[y = \sin x\] at the point (0,0) ?


The point on the curve y2 = x where tangent makes 45° angle with x-axis is ______________ .


The angle between the curves y2 = x and x2 = y at (1, 1) 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 parabolas y2 = 4 ax and x2 = 4ay at the origin is ____________ .


Any tangent to the curve y = 2x7 + 3x + 5 __________________ .


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 y2 = x and x2 = y.


The equation of the normal to the curve y = sinx at (0, 0) is ______.


The tangent to the curve y = x2 + 3x will pass through the point (0, -9) if it is drawn at the point ____________.


Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is parallel to the line 2x − y + 9 = 0.


Which of the following represent the slope of normal?


Find the points on the curve `y = x^3` at which the slope of the tangent is equal to the y-coordinate of the point


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 ______.


For the curve y2 = 2x3 – 7, the slope of the normal at (2, 3) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×