Long Answer TypeFind the equation of the tangent line to the curve y = x2 – 2x + 7 which is
(a) parallel to the line 2x – y + 9 = 0
(ii) perpendicular to the line 5y – 15y = 13
At what point will the tangent to the curve y = 2x3 – 15x2 + 36x – 21 be parallel to x-axis ? Also, find the equations of tangents to the curve at those points.
Short Answer TypeFind the points on the curve x2 + y2 -2x – 3 = 0 at which the tangents are parallel to the x-axis.
Find point on the curve y = 3x2 – 12x + 6 at which tangent is parallel to x-axis. Also find the equation of tangent line.
Find out on the curve y = x2 – x – 8 at which tangent is parallel to x-axis. Also find the equation of tangent line.
Find out on the curve y = 2 x2 – 6x – 4 at which tangent is parallel to x-axis. Also find the equation of tangent line.
Long Answer TypeFind out the points on the curve 
at which the tangents are (i) parallel to the x-axis and (ii) parallel to the y-axis.
The equation of curve is 
Differentiating both sides w.r.t.x, we get,
(i) For the points on the curve, where tangents are parallel to x-axis.
Putting x = 0 in (1), we get,
there is no real point at which the tangent is parallel to x-axis.
(ii) For the points on the curve, where tangents are parallel to y-axis.
Putting y = 0 in (1), we get,
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