If tangent to the curve y 2 + 3x − 7 = 0 at the point (ℎ, k) is parallel to line x − y = 4, then value of k is ______?

If tangent to the curve y^2 + 3x − 7 = 0 at point (h, k) is parallel

Question 14 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 2
Question 14 (OR 1st Question) - CBSE Class 12 Sample Paper for 2020 Boards - Part 3

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Question 14 (OR 1st Question) If tangent to the curve y2 + 3x − 7 = 0 at the point (ℎ, k) is parallel to line x − y = 4, then value of k is ______? We know that Slope of tangent is 𝑑𝑦/𝑑𝑥 Now, y2 + 3x − 7 = 0 Differentiating w.r.t.𝑥 2y𝑑𝑦/𝑑𝑥 + 3 – 0 = 0 2y𝑑𝑦/𝑑𝑥 + 3 = 0 2y𝑑𝑦/𝑑𝑥 = –3 𝑑𝑦/𝑑𝑥 = (−3)/2𝑦 At point (h, k) Slope is 𝑑𝑦/𝑑𝑥 = (−3)/2𝑘 Now, finding slope of line x − y = 4 x − y = 4 x – 4 = y y = x – 4 Comparing with y = mx + c So, slope of line is 1 Since tangent and line are parallel Slope of tangent = 1 𝑑𝑦/𝑑𝑥 = 1 (−3)/2𝑘 = 1 –3 = 2k (−3)/2 = k k = (−𝟑)/𝟐

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.