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Find the Equations of All Lines Having Slope 0 Which Are Tangent to the Curve Y = `1/(X^2-2x + 3)` - Mathematics

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प्रश्न

Find the equations of all lines having slope 0 which are tangent to the curve  y =   `1/(x^2-2x + 3)`

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उत्तर

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पाठ 6: Application of Derivatives - Exercise 6.3 [पृष्ठ २१२]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 6 Application of Derivatives
Exercise 6.3 | Q 12 | पृष्ठ २१२

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

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 slope of the tangent to curve y = x3 − + 1 at the point whose x-coordinate is 2.


Find the slope of the normal to the curve x = acos3θy = asin3θ at `theta = pi/4`


Prove that the curves x = y2 and xy = k cut at right angles if 8k2 = 1. [Hint: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]


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`


The line y = mx + 1 is a tangent to the curve y2 = 4x if the value of m is

(A) 1

(B) 2

(C) 3

(D) 1/2


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 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 points on the curve y2 = 2x3 at which the slope of the tangent is 3 ?


Who that the tangents to the curve y = 7x3 + 11 at the points x = 2 and x = −2 are parallel ?


Find the equation of the tangent and the normal to the following curve at the indicated point  y2 = 4x at (1, 2)  ?


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 \[x = \frac{2 a t^2}{1 + t^2}, y = \frac{2 a t^3}{1 + t^2}\text { at } t = \frac{1}{2}\] ?


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 x2 = y and x3 + 6y = 7 at (1, 1) ?


Find the coordinates of the point on the curve y2 = 3 − 4x where tangent is parallel to the line 2x + y− 2 = 0 ?


Write the angle between the curves y = e−x and y = ex at their point of intersections ?


Write the equation of the normal to the curve y = cos x at (0, 1) ?


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


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


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


If the line y = x touches the curve y = x2 + bx + c at a point (1, 1) then _____________ .


If the curves y = 2 ex and y = ae−x intersect orthogonally, then a = _____________ .


The point on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes is

(a) \[\left( 4, \frac{8}{3} \right)\]

(b) \[\left( - 4, \frac{8}{3} \right)\]

(c) \[\left( 4, - \frac{8}{3} \right)\]

(d) none of these

 


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


The normal at the point (1, 1) on the curve 2y + x2 = 3 is _____________ .


Find the angle of intersection of the curves y = 4 – x2 and y = x2.


The two curves x3 - 3xy2 + 5 = 0 and 3x2y - y3 - 7 = 0


The tangent to the curve y = 2x2 - x + 1 is parallel to the line y = 3x + 9 at the point ____________.


The line y = x + 1 is a tangent to the curve y2 = 4x 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.


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 slope of the tangentto the curve `x= t^2 + 3t - 8, y = 2t^2 - 2t - 5` at the point `(2, -1)` is


The normal at the point (1, 1) on the curve `2y + x^2` = 3 is


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 ______.


If the tangent to the conic, y – 6 = x2 at (2, 10) touches the circle, x2 + y2 + 8x – 2y = k (for some fixed k) at a point (α, β); then (α, β) is ______.


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


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