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 ______.
पर्याय
0
`pi/4`
`pi/3`
`pi/2`
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 points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis.
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 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 = (sin 2x + cot x + 2)2 at x = π/2 ?
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 \[\frac{x^2}{4} + \frac{y^2}{25} = 1\] at which the tangent is parallel to the x-axis ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[c^2 \left( x^2 + y^2 \right) = x^2 y^2 \text { at }\left( \frac{c}{\cos\theta}, \frac{c}{\sin\theta} \right)\] ?
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 and the normal to the following curve at the indicated point x2 = 4y at (2, 1) ?
Find the equation of the normal to the curve ay2 = x3 at the point (am2, am3) ?
Find the equations of all lines of slope zero and that are tangent to the curve \[y = \frac{1}{x^2 - 2x + 3}\] ?
At what points will be tangents to the curve y = 2x3 − 15x2 + 36x − 21 be parallel to x-axis ? Also, find the equations of the tangents to the curve at these points ?
Find the angle of intersection of the following curve \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and x2 + y2 = ab ?
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 slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at t = 2 ?
Write the equation of the normal to the curve y = x + sin x cos x at \[x = \frac{\pi}{2}\] ?
Write the slope of the normal to the curve \[y = \frac{1}{x}\] at the point \[\left( 3, \frac{1}{3} \right)\] ?
Find the equation of the tangent line to the curve `"y" = sqrt(5"x" -3) -5`, which is parallel to the line `4"x" - 2"y" + 5 = 0`.
Find the equation of tangent to the curve `y = sqrt(3x -2)` which is parallel to the line 4x − 2y + 5 = 0. Also, write the equation of normal to the curve at the point of contact.
Find the angle of intersection of the curves y2 = 4ax and x2 = 4by.
Show that the equation of normal at any point on the curve x = 3cos θ – cos3θ, y = 3sinθ – sin3θ is 4 (y cos3θ – x sin3θ) = 3 sin 4θ
The equation of the normal to the curve y = sinx at (0, 0) is ______.
Prove that the curves y2 = 4x and x2 + y2 – 6x + 1 = 0 touch each other at the point (1, 2)
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 – 2 = 0 intersect at an angle of ______.
The point on the curves y = (x – 3)2 where the tangent is parallel to the chord joining (3, 0) and (4, 1) is ____________.
The number of common tangents to the circles x2 + y2 – 4x – 6x – 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 is
The line is y = x + 1 is a tangent to the curve y2 = 4x at the point.
If m be the slope of a tangent to the curve e2y = 1 + 4x2, then ______.
