Advertisements
Advertisements
प्रश्न
The tangent to the curve given by x = et . cost, y = et . sint at t = `pi/4` makes with x-axis an angle ______.
विकल्प
0
`pi/4`
`pi/3`
`pi/2`
Advertisements
उत्तर
The tangent to the curve given by x = et . cost, y = et . sint at t = `pi/4` makes with x-axis an angle `pi/2`.
Explanation:
`"dx"/"dt"` = – et . sint + etcost
`"dy"/"dt" = etcost + etsint
Therefore, `("dy"/"dx")_("t" = pi/4) = (cos"t" + sin"t")/(cos"t" - sin"t") = sqrt(2)/0`
APPEARS IN
संबंधित प्रश्न
Find the slope of the tangent to the curve y = 3x4 − 4x at x = 4.
Find the equations of all lines having slope 0 which are tangent to the curve y = `1/(x^2-2x + 3)`
Find the equation of the normal at the point (am2, am3) for the curve ay2 = x3.
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 \[y = \sqrt{x} \text { at }x = 9\] ?
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 x2 + 3y + y2 = 5 at (1, 1) ?
Find the points on the curve 2a2y = x3 − 3ax2 where the tangent is parallel to x-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 to the curve x = θ + sin θ, y = 1 + cos θ at θ = π/4 ?
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 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 line to the curve y = x2 − 2x + 7 which perpendicular to the line 5y − 15x = 13. ?
Find the angle of intersection of the following curve x2 = 27y and y2 = 8x ?
Show that the following set of curve intersect orthogonally y = x3 and 6y = 7 − x2 ?
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 \[\left( 1, 2\sqrt{2} \right)\] ?
Show that the curves \[\frac{x^2}{a^2 + \lambda_1} + \frac{y^2}{b^2 + \lambda_1} = 1 \text { and } \frac{x^2}{a^2 + \lambda_2} + \frac{y^2}{b^2 + \lambda_2} = 1\] intersect at right angles ?
Find the point on the curve y = x2 − 2x + 3, where the tangent is parallel to x-axis ?
Find the slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at t = 2 ?
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 equation on the tangent to the curve y = x2 − x + 2 at the point where it crosses the y-axis ?
The point on the curve y = x2 − 3x + 2 where tangent is perpendicular to y = x is ________________ .
The angle between the curves y2 = x and x2 = y at (1, 1) is ______________ .
The curves y = aex and y = be−x cut orthogonally, if ___________ .
Any tangent to the curve y = 2x7 + 3x + 5 __________________ .
Find the angle of intersection of the curves y2 = x and x2 = y.
Find the angle of intersection of the curves y = 4 – x2 and y = x2.
Prove that the curves y2 = 4x and x2 + y2 – 6x + 1 = 0 touch each other at the point (1, 2)
The tangent to the curve y = e2x at the point (0, 1) meets x-axis at ______.
Find points on the curve `x^2/9 + "y"^2/16` = 1 at which the tangent is parallel to y-axis.
The number of common tangents to the circles x2 + y2 – 4x – 6x – 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 is
The normal at the point (1, 1) on the curve `2y + x^2` = 3 is
The normals to the curve x = a(θ + sinθ), y = a(1 – cosθ) at the points θ = (2n + 1)π, n∈I are all ______.
