Short Answer TypeFind the point on the curve y = x3 – 2x2 – 2x at which the tangent lines are parallel to the line y = 2x – 3.
Find the points on the curve y = x3 – 2x2 – x at which the tangent lines are parallel to the line y = 3x – 2.
Find the equation of the tangent to the curve x2 + 3y = 3, which is parallel to the line y – 4x + 5 = 0.
Find the equation of all lines having slope 2 and being tangent to the curve 
.
The equation of curve is
or 
there are two tangents to the given curve with slope 2 and passing through the points (2, 2) and (4, -2).
The equation of line through (2, 2) is
y – 2 = 2 (x – 2) or y – 2 = 2x – 4 or 2 x – 2 = 0
The equation of line through (4, – 2) is
y – (– 2) = 2 (x – 4) or y + 2 = 2 x – 8 or 2 x – y – 10 = 0
Long Answer TypeShort Answer TypeFind the equation of the tangent to the curve 
which is parallel to the line 4x - 2y + 5 = 0
Long Answer TypeFind the equation of tangents to the curve
y = cos (x + y), – 2 
≤ x ≤ 2 
that are parallel to the line x + 2y = 0.
Find the point on curve 4x2 + 9y2 = 1, where the tangents are perpendicular to the line 2y + x = 0.
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