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

If tangent to the curve y^2 + 3x βˆ’ 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


Transcript

Question 14 (OR 1st Question) If tangent to the curve y2 + 3x βˆ’ 7 = 0 at the point (β„Ž, k) is parallel to line x βˆ’ y = 4, then value of k is ______? We know that Slope of tangent is 𝑑𝑦/𝑑π‘₯ Now, y2 + 3x βˆ’ 7 = 0 Differentiating w.r.t.π‘₯ 2y𝑑𝑦/𝑑π‘₯ + 3 – 0 = 0 2y𝑑𝑦/𝑑π‘₯ + 3 = 0 2y𝑑𝑦/𝑑π‘₯ = –3 𝑑𝑦/𝑑π‘₯ = (βˆ’3)/2𝑦 At point (h, k) Slope is 𝑑𝑦/𝑑π‘₯ = (βˆ’3)/2π‘˜ Now, finding slope of line x βˆ’ y = 4 x βˆ’ 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/𝑑π‘₯ = 1 (βˆ’3)/2π‘˜ = 1 –3 = 2k (βˆ’3)/2 = k k = (βˆ’πŸ‘)/𝟐

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.