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 equations of all lines having slope -1 that are tangents to the curve 
The equations of the curve is 
∴ there are two tangents to the given curve with slope – 1 and passing through the points (0, – 1) and (2, 1).
The equation of tangent through (0, – 1) is
y – (– 1) = – 1 (x – 0) or y + 1 = – x or x + y + 1 = 0
The equation of tangent through (2, 1) is
y – 1 = – 1 (x – 2) or y – 1 = – x + 2 or x + y – 3 = 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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