Advertisements
Advertisements
प्रश्न
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x2 at (0, 0)
उत्तर
The equation of the curve is y = x2.
On differentiating with respect to x, we get:
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.
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 = x3 − 3x + 2 at the point whose x-coordinate is 3.
Find the equation of all lines having slope 2 which are tangents to the curve `y = 1/(x- 3), x != 3`
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 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 values of a and b if the slope of the tangent to the curve xy + ax + by = 2 at (1, 1) is 2 ?
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 x2 + y2 = 13, the tangent at each one of which is parallel to the line 2x + 3y = 7 ?
Find the points on the curve \[\frac{x^2}{4} + \frac{y^2}{25} = 1\] at which the tangent is parallel to the x-axis ?
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 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 = at2, y = 2at at t = 1 ?
Find the equation of the normal to the curve x2 + 2y2 − 4x − 6y + 8 = 0 at the point whose abscissa is 2 ?
Find the equation of the tangent to the curve x2 + 3y − 3 = 0, which is parallel to the line y= 4x − 5 ?
Find the equation of the tangent to the curve x = sin 3t, y = cos 2t at
\[t = \frac{\pi}{4}\] ?
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 y = x3 and 6y = 7 − x2 ?
Show that the curves 2x = y2 and 2xy = k cut at right angles, if k2 = 8 ?
Find the slope of the normal at the point 't' on the curve \[x = \frac{1}{t}, y = t\] ?
Write the angle made by the tangent to the curve x = et cos t, y = et sin t at \[t = \frac{\pi}{4}\] with the x-axis ?
Write the slope of the normal to the curve \[y = \frac{1}{x}\] at the point \[\left( 3, \frac{1}{3} \right)\] ?
The equation to the normal to the curve y = sin x at (0, 0) is ___________ .
The equation of the normal to the curve y = x + sin x cos x at x = `π/2` is ___________ .
The equation of the normal to the curve y = x(2 − x) at the point (2, 0) is ________________ .
The angle of intersection of the curves xy = a2 and x2 − y2 = 2a2 is ______________ .
The angle of intersection of the parabolas y2 = 4 ax and x2 = 4ay at the origin 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 ______.
Find the condition that the curves 2x = y2 and 2xy = k intersect orthogonally.
The equation of normal to the curve 3x2 – y2 = 8 which is parallel to the line x + 3y = 8 is ______.
The points at which the tangents to the curve y = x3 – 12x + 18 are parallel to x-axis are ______.
The points on the curve `"x"^2/9 + "y"^2/16` = 1 at which the tangents are parallel to the y-axis are:
The tangent to the curve y = x2 + 3x will pass through the point (0, -9) if it is drawn at the point ____________.
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:
The points at which the tangent passes through the origin for the curve y = 4x3 – 2x5 are
Let `y = f(x)` be the equation of the curve, then equation of normal is
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 ______.
