Advertisements
Advertisements
प्रश्न
Find the point on the curve y = x3 − 11x + 5 at which the tangent is y = x − 11.
उत्तर
The equation of the given curve is y = x3 − 11x + 5.
The equation of the tangent to the given curve is given as y = x − 11 (which is of the form y = mx + c).
∴Slope of the tangent = 1
When x = 2, y = (2)3 − 11 (2) + 5 = 8 − 22 + 5 = −9.
When x = −2, y = (−2)3 − 11 (−2) + 5 = −8 + 22 + 5 = 19.
Hence, the required points are (2, −9) and (−2, 19).
But, both these points should satisfy the equation of the tangent as there would be point of contact between tangent and the curve.
∴ (2, −9) is the required point as (−2, 19) is not satisfying the given equation of tangent.
APPEARS IN
संबंधित प्रश्न
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 equation of all lines having slope 2 which are tangents to the curve `y = 1/(x- 3), x != 3`
Show that the tangents to the curve y = 7x3 + 11 at the points where x = 2 and x = −2 are parallel.
For the curve y = 4x3 − 2x5, find all the points at which the tangents passes through the origin.
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 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 2a2y = x3 − 3ax2 where the tangent is parallel to x-axis ?
At what points on the curve y = x2 − 4x + 5 is the tangent perpendicular to the line 2y + x = 7?
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 \[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text { at } \left( x_0 , y_0 \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated points:
x = 3cosθ − cos3θ, y = 3sinθ − sin3θ?
Find the equation of the tangent and the normal to the following curve at the indicated points x = asect, y = btant at t ?
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 x = sin 3t, y = cos 2t at
\[t = \frac{\pi}{4}\] ?
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 x2 + 4y2 = 8 and x2 − 2y2 = 2 ?
Show that the following set of curve intersect orthogonally x2 + 4y2 = 8 and x2 − 2y2 = 4 ?
Find the condition for the following set of curve to intersect orthogonally \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \text { and } \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1\] ?
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 \[\alpha\] \[-\] b2sin2 \[\alpha\] = p2 ?
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 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 coordinates of the point at which the tangent to the curve y = 2x2 − x + 1 is parallel to the line y = 3x + 9 ?
If the curve ay + x2 = 7 and x3 = y cut orthogonally at (1, 1), then a is equal to _____________ .
The curves y = aex and y = be−x cut orthogonally, if ___________ .
The point on the curve y = 6x − x2 at which the tangent to the curve is inclined at π/4 to the line x + y= 0 is __________ .
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`.
The abscissa of the point on the curve 3y = 6x – 5x3, the normal at which passes through origin is ______.
The equation of the normal to the curve y = sinx at (0, 0) is ______.
Find a point on the curve y = (x – 2)2. at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).
Tangent is drawn to the ellipse `x^2/27 + y^2 = 1` at the point `(3sqrt(3) cos theta, sin theta), 0 < 0 < 1`. The sum of the intercepts on the axes made by the tangent is minimum if 0 is equal to
The number of common tangents to the circles x2 + y2 – 4x – 6x – 12 = 0 and x2 + y2 + 6x + 18y + 26 = 0 is
The points at which the tangent passes through the origin for the curve y = 4x3 – 2x5 are
Which of the following represent the slope of normal?
If the tangent to the curve y = x + siny at a point (a, b) is parallel to the line joining `(0, 3/2)` and `(1/2, 2)`, then ______.
The normals to the curve x = a(θ + sinθ), y = a(1 – cosθ) at the points θ = (2n + 1)π, n∈I are all ______.
For the curve y2 = 2x3 – 7, the slope of the normal at (2, 3) is ______.
