Question

# Find the equation of the tangent line to the curve which is. (a) parallel to the line . (b) perpendicular to the line

Medium
Updated on : 2022-09-05
Solution
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## (a)The equation of the given curve is  . On differentiating with respect to , we get:  The equation of the line is This is of the form Slope of the line If a tangent is parallel to the line , then the slope of the tangent is equal to the slope of the line. Therefore, we have: Now, at Thus, the equation of the tangent passing through is given by,  Hence, the equation of the tangent line to the given curve (which is parallel to line is (b)The equation of the line is Slope of the line If a tangent is perpendicular to the line ,  then the slope of the tangent is . Now, at  Thus, the equation of the tangent passing through  is given by,        Hence, the equation of the tangent line to the given curve  (which is perpendicular to line is

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