CBSE Class 12 Sample Paper for 2020 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## If tangent to the curve y 2 + 3x β 7 = 0 at the point (β, k) is parallel to line x β y = 4, then value of k is ______?

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Question 14 (OR 1st Question) If tangent to the curve y2 + 3x β 7 = 0 at the point (β, k) is parallel to line x β y = 4, then value of k is ______? We know that Slope of tangent is ππ¦/ππ₯ Now, y2 + 3x β 7 = 0 Differentiating w.r.t.π₯ 2yππ¦/ππ₯ + 3 β 0 = 0 2yππ¦/ππ₯ + 3 = 0 2yππ¦/ππ₯ = β3 ππ¦/ππ₯ = (β3)/2π¦ At point (h, k) Slope is ππ¦/ππ₯ = (β3)/2π Now, finding slope of line x β y = 4 x β y = 4 x β 4 = y y = x β 4 Comparing with y = mx + c So, slope of line is 1 Since tangent and line are parallel Slope of tangent = 1 ππ¦/ππ₯ = 1 (β3)/2π = 1 β3 = 2k (β3)/2 = k k = (βπ)/π