Advertisements
Advertisements
प्रश्न
Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is parallel to the line 2x − y + 9 = 0.
Advertisements
उत्तर
The equation of the given curve is y = x2 − 2x + 7
On differentiating with respect to x, we get:
`"dy"/"dx" = 2x - 2`
The equation of the line is 2x − y + 9 = 0.
2x − y + 9 = 0 ⇒ y = 2x + 9
This is of the form y = mx + c.
∴ Slope of the line = 2
If a tangent is parallel to the line 2x − y + 9 = 0, then the slope of the tangent is equal to the slope of the line.
Therefore, we have:
2 = 2x − 2
⇒ 2x = 4
⇒ x = 2
Now, x = 2
⇒ y = 4 - 4 + 7 = 7
Thus, the equation of the tangent passing through passing through (2, 7) is given by,
⇒ y - 7 = 2 (x - 2)
⇒ y - 2x - 3 = 0
Hence, the equation of the tangent line to the given curve (which is parallel to line 2x - y + 9 = 0) is y - 2x - 3 = 0.
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 slope of the tangent to the curve y = 3x4 − 4x at x = 4.
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).
Find the equation of all lines having slope −1 that are tangents to the curve `y = 1/(x -1), x != 1`
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x3 at (1, 1)
Find the equations of the tangent and normal to the given curves at the indicated points:
x = cos t, y = sin t at t = `pi/4`
Find the points on the curve x2 + y2 − 2x − 3 = 0 at which the tangents are parallel to the x-axis.
Find the equation of the normals to the curve y = x3 + 2x + 6 which are parallel to the line x + 14y + 4 = 0.
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`
At what points on the circle x2 + y2 − 2x − 4y + 1 = 0, the tangent is parallel to x-axis?
Find the equation of the normal to y = 2x3 − x2 + 3 at (1, 4) ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = x2 at (0, 0) ?
Find the equation of the tangent and the normal to the following curve at the indicated point \[y^2 = \frac{x^3}{4 - x}at \left( 2, - 2 \right)\] ?
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 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 an equation of normal line to the curve y = x3 + 2x + 6 which is parallel to the line x+ 14y + 4 = 0 ?
Prove that the curves xy = 4 and x2 + y2 = 8 touch each other ?
If the tangent line at a point (x, y) on the curve y = f(x) is parallel to x-axis, then write the value of \[\frac{dy}{dx}\] ?
Write the value of \[\frac{dy}{dx}\] , if the normal to the curve y = f(x) at (x, y) is parallel to y-axis ?
If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of \[\frac{dx}{dy}\] ?
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 ?
The equation to the normal to the curve y = sin x at (0, 0) is ___________ .
The equations of tangent at those points where the curve y = x2 − 3x + 2 meets x-axis are _______________ .
If the line y = x touches the curve y = x2 + bx + c at a point (1, 1) then _____________ .
The slope of the tangent to the curve x = 3t2 + 1, y = t3 −1 at x = 1 is ___________ .
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 __________ .
The angle of intersection of the curves y = 2 sin2 x and y = cos 2 x at \[x = \frac{\pi}{6}\] is ____________ .
Find the equation of the normal lines to the curve 3x2 – y2 = 8 which are parallel to the line x + 3y = 4.
At what points on the curve x2 + y2 – 2x – 4y + 1 = 0, the tangents are parallel to the y-axis?
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 – 2 = 0 intersect at an angle of ______.
`"sin"^"p" theta "cos"^"q" theta` attains a maximum, when `theta` = ____________.
Find points on the curve `x^2/9 + "y"^2/16` = 1 at which the tangent is parallel to y-axis.
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 slope of the tangentto the curve `x= t^2 + 3t - 8, y = 2t^2 - 2t - 5` at the point `(2, -1)` is
If (a, b), (c, d) are points on the curve 9y2 = x3 where the normal makes equal intercepts on the axes, then the value of a + b + c + d is ______.
Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, From this horizontal plane is ______.
