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

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Transcript

Question 14 (OR 1st Question) If tangent to the curve y2 + 3x โˆ’ 7 = 0 at the point (โ„Ž, k) is parallel to line x โˆ’ y = 4, then value of k is ______? We know that Slope of tangent is ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ Now, y2 + 3x โˆ’ 7 = 0 Differentiating w.r.t.๐‘ฅ 2y๐‘‘๐‘ฆ/๐‘‘๐‘ฅ + 3 โ€“ 0 = 0 2y๐‘‘๐‘ฆ/๐‘‘๐‘ฅ + 3 = 0 2y๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = โ€“3 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (โˆ’3)/2๐‘ฆ At point (h, k) Slope is ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (โˆ’3)/2๐‘˜ Now, finding slope of line x โˆ’ y = 4 x โˆ’ y = 4 x โ€“ 4 = y y = x โ€“ 4 So, slope of line is 1 Since tangent and line are parallel Slope of tangent = 1 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1 (โˆ’3)/2๐‘˜ = 1 โ€“3 = 2k (โˆ’3)/2 = k k = (โˆ’๐Ÿ‘)/๐Ÿ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.